/handwritten notes of stress strain curve
Searching Images
stress strain curve diagram engineering materials
This composite educational graphic illustrates the mechanical and morphological properties of 3D-printed polylactic acid (PLA) and cellulose nanofiber (CNF) composites, materials frequently investigated for biomedical applications such as tissue engineering scaffolds and orthopedic implants. Panels (a-c) present quantitative mechanical data. A tensile stress-strain curve (a) compares compression-molded versus 3D-printed variants, highlighting differences in tensile strength and elongation. Histograms (b-c) detail elongation (%), tensile strength (MPa), and Young's modulus (MPa), demonstrating that 1% CNF reinforcement enhances the mechanical robustness of 3D-printed structures. Panels (d-g) show Scanning Electron Microscopy (SEM) micrographs of tensile fracture surfaces. Micrographs (d) and (e) (magnifications x150 and x600) show neat 3D-printed PLA, characterized by visible voids and overlapped structures (arrows) indicating lower structural integrity. In contrast, micrographs (f) and (g) display 3D-printed PLA/1% CNF composites, revealing a more uniform, densely packed morphology with fewer structural defects. These visuals demonstrate how nanocellulose integration improves the microstructural bonding and mechanical performance of biocompatible 3D-printed constructs.
This infographic and computational diagram illustrate a 3D Finite Element Analysis (FEA) of a human vertebral column with scoliosis. The main visual features a mesh-based structural model of the spine against a blue background, displaying the characteristic lateral curvature of scoliosis. Color-coded heat mapping on the intervertebral discs and vertebrae indicates stress distribution, with green, yellow, and red zones representing increasing mechanical strain; a 'Max' tag identifies the peak stress point, typically near inflection points of the spinal curve. Below the 3D model, two circular inset diagrams provide a schematic breakdown of the 'Series System' and 'Parallel System' used for reliability modeling. These diagrams define the vertebra as a combination of cortical and cancellous bone, and the intervertebral disc as a combination of the annulus fibrosus and nucleus pulposus. Mathematical formulas for probability of failure (Pf) are interspersed, detailing sectional and total backbone reliability calculations. This visual is designed for advanced biomechanical engineering and orthopedic research contexts to assess structural integrity and system reliability in spinal disorders.
This composite educational graphic illustrates the mechanical properties and strain evolution of a mycelium-based biomaterial under uniaxial compression. Part (a) displays a true stress (kPa) versus true strain curve, identifying six specific points (A-F) that represent stages from linear elastic response to yielding and strain hardening. Part (b) presents a corresponding sequence of digital image correlation (DIC) maps for each point. These maps visualize the logarithmic normal strain distribution using a color-coded scale ranging from red (positive/low strain, ~0.01) to blue (significant negative strain, ~-0.08). The sequence demonstrates the progression from a uniform strain state (A) to the initiation of strain localization (B-C) and the final formation of distinct, diagonal 'collapse bands' (D-F). This illustrates how the stochastic, porous network structure of the mycelium fiber network leads to heterogeneous deformation and structural yielding, a key concept in biomaterial engineering and the study of biofoam mechanics for medical or structural applications.
A multi-panel scientific infographic and diagram set illustrating the mechanical and luminescent performance of a Hydroscopic Induced Dual-network Polymer (HIDP), a material designed for biocompatible ionotronics and electronic skins. (a) and (f) present clinical-style photographic sequences of the HIDP and a pre-notched HIDP under tensile strain from 0% to 700%, demonstrating significant vertical elongation, central necking, and sustained blue luminescence. (b) displays a J-shaped true stress-elongation curve, comparing HIDP to biological skin, rubber, and thermoplastics. (c) is an Ashby plot comparing Young’s modulus and strain of failure, positioning HIDP near biological tissues like elastin, skin, and muscles. (d) shows photographic evidence of luminescence stability after 100 stretching cycles at 200% strain. (e) provides an Ashby plot for fracture toughness versus hysteresis, comparing HIDP to DN hydrogels and PDMS. (g) shows a tensile stress-strain curve indicating ductile fracture behavior. (h) demonstrates the material's self-healing properties through a dual-color blue and green luminescent HIDP assembly at 0% and 300% strain. This content is intended for research in biomedical engineering, prosthetics, and wearable medical sensors.
This line graph illustrates the piezoresistive behavior of a carbon nanotube (CNT) polymer composite, a material technology utilized in medical pressure sensors and bio-mechanical monitoring. The plot tracks two variables over a 120-second interval: cyclic displacement (red line) and resistance variation (blue line). The red curve depicts a regular mechanical oscillation between 0.0 and 2.5 mm, simulating repetitive stress or movement. The blue curve represents the resulting resistance variation percentage (%), demonstrating the material's sensitivity to physical deformation. A clear inverse correlation is visible: as displacement peaks (maximum strain), the resistance variation reaches a valley, indicating a decrease in electrical resistance. The data shows high reproducibility with a slight attenuation in resistance amplitude over time, reaching a stable cyclical state. This relationship is critical for biomedical engineering applications where such materials serve as strain gauges for monitoring physiological signals like gait, respiration, or joint mobility.
A scientific infographic and plot illustrating the biomechanical properties and morphology of a 0.9A cellulose acetate aerogel, a material studied for tissue engineering and medical scaffolding applications. The primary graph displays compressive Stress (kPa) vs. Strain (mm/mm) comparing in-plane (solid red line) and out-of-plane (dashed black line) compression. The in-plane curve exhibits a distinct linear elastic region, yielding at approximately 15% strain, followed by a plateau and sharp densification after 74% strain. The out-of-plane curve shows lower initial stress with densification occurring at 86% strain. Insets provide Scanning Electron Microscopy (SEM) micrographs (200 µm scale) and clinical-style macro photographs of the samples. The 'Uncompressed' SEM shows a regular honeycomb-like pore structure; 'Out-of-plane' compression results in pore wall bending and minor cracking; 'In-plane' compression leads to total structural collapse and loss of pore morphology. Schematic diagrams illustrate the directional force applied relative to the longitudinal pore alignment, highlighting the material's anisotropic mechanical behavior relevant to structural biomaterials.
Searching the Web
stress strain curve handwritten notes engineering materials science
Loading Image
Loading Image
Generating Image
Handwritten-style engineering notes of a stress-strain curve for mild steel (low carbon steel), showing all key labeled regions: Proportional Limit, Elastic Limit, Upper Yield Point, Lower Yield Point, Ultimate Tensile Strength (UTS), Fracture Point. Include the following zones clearly labeled: Elastic Region, Plastic Region, Strain Hardening, Necking. Show axes labeled Stress (σ) on Y-axis and Strain (ε) on X-axis. Add handwritten annotation notes beside each point explaining what it means. Also include a smaller inset sketch comparing ductile vs brittle material curves. Style should look like neat hand-drawn pencil notes on white paper with annotations, like a student's engineering study notes.
Here's a reference diagram showing Engineering vs True stress-strain curves:
Stress-Strain Curve - Complete Notes
What is it?
A graph plotting Stress (σ) on the Y-axis vs Strain (ε) on the X-axis, obtained from a tensile test. It reveals key mechanical properties of a material.
- Stress (σ) = Force / Original Cross-sectional Area (Pa or MPa)
- Strain (ε) = Change in Length / Original Length (dimensionless)
Key Points on the Curve (Mild Steel / Ductile Metal)
| Point | Name | Description |
|---|---|---|
| O-A | Proportional Limit | Stress ∝ Strain (Hooke's Law holds). The curve is a straight line. |
| A | Elastic Limit | Maximum stress up to which material returns to original shape on load removal. |
| B | Upper Yield Point | Sudden drop in stress; dislocations begin to move. |
| C | Lower Yield Point | Stress at which yielding continues at constant (or lower) stress. |
| D | Ultimate Tensile Strength (UTS) | Maximum stress the material can withstand before necking begins. |
| E | Fracture / Breaking Point | Material breaks. |
Zones on the Curve
- Elastic Region (O to A): Deformation is reversible. Young's modulus (E) = slope of this line.
- Yield Zone (B-C): Plastic deformation begins. Upper and lower yield points visible in mild steel.
- Strain Hardening (C to D): Material strengthens due to dislocation pile-up; stress increases again.
- Necking (D to E): Cross-sectional area reduces locally; engineering stress appears to drop, but true stress keeps rising.
Important Formulae
- Young's Modulus: E = σ / ε (slope of elastic region)
- Resilience: Area under elastic region = energy stored per unit volume
- Toughness: Total area under the curve = energy absorbed before fracture
Ductile vs Brittle Materials
| Property | Ductile (e.g., Steel, Aluminium) | Brittle (e.g., Cast iron, Glass) |
|---|---|---|
| Plastic deformation | Large | Very small / none |
| Fracture | After necking | Sudden, without warning |
| Curve shape | Long curve with yield + UTS regions | Short, nearly linear until fracture |
| Example use | Structural beams, car bodies | Engine blocks, ceramics |
Engineering vs True Stress-Strain
- Engineering stress/strain uses the original dimensions - easier to measure.
- True stress/strain uses instantaneous dimensions - more accurate, especially post-necking.
- True stress is always higher than engineering stress after yielding begins.
Key takeaway: The stress-strain curve is the foundation of materials selection in engineering - it tells you if a material is stiff, strong, ductile, tough, or brittle at a glance.
Create a PDF quick reference guide for stress-strain curves
Reading File
Reading File
Running Command
ls -la /tmp/workspace/ 2>/dev/null || echo "workspace does not exist"
Running Command
mkdir -p /tmp/workspace/stress-strain-pdf
Writing File
~/stress-strain-pdf/build_pdf.py
"""
Stress-Strain Curve Quick Reference Guide PDF
Using reportlab with matplotlib for the curve diagrams
"""
import os
import math
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt
import matplotlib.patches as mpatches
import numpy as np
from reportlab.lib.pagesizes import A4
from reportlab.lib import colors
from reportlab.lib.units import mm, cm
from reportlab.lib.styles import getSampleStyleSheet, ParagraphStyle
from reportlab.lib.enums import TA_CENTER, TA_LEFT, TA_JUSTIFY
from reportlab.platypus import (
SimpleDocTemplate, Paragraph, Spacer, Table, TableStyle,
HRFlowable, Image, KeepTogether
)
from reportlab.lib.colors import HexColor
OUTPUT_DIR = "/tmp/workspace/stress-strain-pdf"
PDF_PATH = os.path.join(OUTPUT_DIR, "Stress_Strain_Quick_Reference.pdf")
IMG_DIR = os.path.join(OUTPUT_DIR, "imgs")
os.makedirs(IMG_DIR, exist_ok=True)
# ─── COLORS ────────────────────────────────────────────────────────────────────
C_NAVY = HexColor("#1a2d5a")
C_BLUE = HexColor("#2563eb")
C_LIGHT = HexColor("#dbeafe")
C_ACCENT = HexColor("#f59e0b")
C_RED = HexColor("#dc2626")
C_GREEN = HexColor("#16a34a")
C_PURPLE = HexColor("#7c3aed")
C_GRAY = HexColor("#6b7280")
C_LGRAY = HexColor("#f3f4f6")
C_WHITE = colors.white
C_BLACK = colors.black
# ─── FIGURE 1: Mild Steel Stress-Strain Curve ─────────────────────────────────
def plot_mild_steel():
fig, ax = plt.subplots(figsize=(8, 5))
fig.patch.set_facecolor('#f8fafc')
ax.set_facecolor('#f8fafc')
# Build the curve piecewise
# O -> A (elastic, linear)
e1 = np.linspace(0, 0.002, 50)
s1 = e1 * 200000 # MPa, slope = E = 200 GPa
# A -> B (upper yield)
e2 = np.linspace(0.002, 0.0022, 10)
s2 = np.linspace(400, 420, 10)
# B -> C (drop to lower yield)
e3 = np.linspace(0.0022, 0.0025, 10)
s3 = np.linspace(420, 360, 10)
# C -> D (yield plateau / Luders band)
e4 = np.linspace(0.0025, 0.012, 20)
s4 = np.linspace(360, 360, 20)
# D -> E (strain hardening, smooth rise)
e5 = np.linspace(0.012, 0.20, 60)
s5 = 360 + 220 * (1 - np.exp(-12 * (e5 - 0.012)))
# E -> F (necking, UTS -> fracture)
e6 = np.linspace(0.20, 0.28, 30)
s6 = s5[-1] - 120 * ((e6 - 0.20) / 0.08) ** 0.7
# Full arrays
e_all = np.concatenate([e1, e2, e3, e4, e5, e6])
s_all = np.concatenate([s1, s2, s3, s4, s5, s6])
ax.plot(e_all * 100, s_all, color='#1a2d5a', lw=2.5, zorder=3)
# Key points
pts = {
'O': (0, 0, 'Origin'),
'A': (0.2, 400, 'Proportional\nLimit'),
'B': (0.22, 420, 'Upper Yield\nPoint'),
'C': (0.25, 360, 'Lower Yield\nPoint'),
'D': (1.2, 360, 'End of Yield\nPlateau'),
'E': (20.0, s5[-1],'UTS'),
'F': (28.0, s6[-1],'Fracture'),
}
label_offsets = {
'O': (-0.5, 20),
'A': (-1.5, 18),
'B': (0.3, 15),
'C': (0.3, -25),
'D': (0.3, -25),
'E': (-2, 15),
'F': (0.3, 10),
}
dot_colors = {
'O': '#6b7280', 'A': '#2563eb', 'B': '#f59e0b',
'C': '#f59e0b', 'D': '#16a34a', 'E': '#dc2626', 'F': '#7c3aed'
}
for key, (ex, sy, lbl) in pts.items():
ax.scatter(ex, sy, color=dot_colors[key], s=60, zorder=5)
dx, dy = label_offsets[key]
ax.annotate(key, (ex, sy), xytext=(ex + dx, sy + dy),
fontsize=9, fontweight='bold', color=dot_colors[key],
ha='center')
# Zone shading
# Elastic region
mask_e = e_all <= 0.002
ax.fill_between(e_all[mask_e]*100, s_all[mask_e], alpha=0.15, color='#2563eb')
ax.text(0.1, 150, 'ELASTIC\nREGION', fontsize=7, color='#2563eb',
ha='center', va='center', style='italic')
# Yield plateau
mask_y = (e_all >= 0.0022) & (e_all <= 0.012)
ax.fill_between(e_all[mask_y]*100, s_all[mask_y], alpha=0.15, color='#f59e0b')
ax.text(0.7, 200, 'YIELD\nPLATEAU', fontsize=7, color='#b45309',
ha='center', va='center', style='italic')
# Strain hardening
mask_sh = (e_all >= 0.012) & (e_all <= 0.20)
ax.fill_between(e_all[mask_sh]*100, s_all[mask_sh], alpha=0.12, color='#16a34a')
ax.text(10, 250, 'STRAIN\nHARDENING', fontsize=7, color='#16a34a',
ha='center', va='center', style='italic')
# Necking
mask_n = e_all >= 0.20
ax.fill_between(e_all[mask_n]*100, s_all[mask_n], alpha=0.15, color='#dc2626')
ax.text(24, 350, 'NECKING', fontsize=7, color='#dc2626',
ha='center', va='center', style='italic')
ax.set_xlabel('Strain ε (%)', fontsize=11, labelpad=6)
ax.set_ylabel('Stress σ (MPa)', fontsize=11, labelpad=6)
ax.set_title('Stress-Strain Curve — Mild Steel (Low Carbon)', fontsize=12,
fontweight='bold', color='#1a2d5a', pad=10)
ax.set_xlim(-0.5, 30)
ax.set_ylim(-20, 620)
ax.spines[['top', 'right']].set_visible(False)
ax.grid(True, linestyle='--', alpha=0.4, color='#cbd5e1')
# Legend patches
patches = [
mpatches.Patch(color='#2563eb', alpha=0.4, label='Elastic Region'),
mpatches.Patch(color='#f59e0b', alpha=0.4, label='Yield Plateau'),
mpatches.Patch(color='#16a34a', alpha=0.4, label='Strain Hardening'),
mpatches.Patch(color='#dc2626', alpha=0.4, label='Necking'),
]
ax.legend(handles=patches, loc='upper left', fontsize=8, framealpha=0.8)
plt.tight_layout()
path = os.path.join(IMG_DIR, "mild_steel_curve.png")
fig.savefig(path, dpi=150, bbox_inches='tight')
plt.close()
return path
# ─── FIGURE 2: Ductile vs Brittle Comparison ──────────────────────────────────
def plot_ductile_brittle():
fig, ax = plt.subplots(figsize=(7, 4))
fig.patch.set_facecolor('#f8fafc')
ax.set_facecolor('#f8fafc')
# Ductile (steel-like)
e_d = np.linspace(0, 0.35, 300)
s_d = np.where(e_d < 0.002,
e_d * 200000,
np.where(e_d < 0.012, 400,
400 + 200 * (1 - np.exp(-10*(e_d - 0.012)))))
# drop after UTS
uts_idx = np.argmax(s_d)
s_d[uts_idx:] = s_d[uts_idx] * (1 - 0.6 * ((e_d[uts_idx:] - e_d[uts_idx]) / (0.35 - e_d[uts_idx]))**0.5)
ax.plot(e_d*100, s_d, color='#2563eb', lw=2.5, label='Ductile (e.g. Steel)')
ax.scatter([e_d[-1]*100], [s_d[-1]], color='#2563eb', s=60, zorder=5)
# Brittle (cast iron-like)
e_b = np.linspace(0, 0.008, 100)
s_b = 300 * np.sin(e_b / 0.008 * math.pi / 2) ** 0.6
ax.plot(e_b*100, s_b, color='#dc2626', lw=2.5, label='Brittle (e.g. Cast Iron)', linestyle='--')
ax.scatter([e_b[-1]*100], [s_b[-1]], color='#dc2626', s=60, zorder=5,
marker='X')
# Rubber/elastomer
e_r = np.linspace(0, 5.0, 200)
s_r = 5 * (e_r / 5)**0.3 * 30
ax.plot(e_r, s_r, color='#16a34a', lw=2, label='Elastomer (e.g. Rubber)', linestyle=':')
ax.annotate('Fracture\n(brittle)', xy=(0.8, s_b[-1]), xytext=(2.5, 200),
arrowprops=dict(arrowstyle='->', color='#dc2626'),
fontsize=8, color='#dc2626', ha='center')
ax.annotate('Fracture\n(ductile)', xy=(35, s_d[-1]), xytext=(27, 180),
arrowprops=dict(arrowstyle='->', color='#2563eb'),
fontsize=8, color='#2563eb', ha='center')
ax.set_xlabel('Strain ε (%)', fontsize=10)
ax.set_ylabel('Stress σ (MPa)', fontsize=10)
ax.set_title('Ductile vs Brittle vs Elastomer', fontsize=11,
fontweight='bold', color='#1a2d5a')
ax.set_xlim(-0.2, 38)
ax.set_ylim(-10, 650)
ax.legend(fontsize=8, framealpha=0.85)
ax.spines[['top','right']].set_visible(False)
ax.grid(True, linestyle='--', alpha=0.4, color='#cbd5e1')
plt.tight_layout()
path = os.path.join(IMG_DIR, "ductile_brittle.png")
fig.savefig(path, dpi=150, bbox_inches='tight')
plt.close()
return path
# ─── FIGURE 3: Engineering vs True Stress-Strain ──────────────────────────────
def plot_eng_vs_true():
fig, ax = plt.subplots(figsize=(6, 4))
fig.patch.set_facecolor('#f8fafc')
ax.set_facecolor('#f8fafc')
e_eng = np.linspace(0, 0.5, 300)
# Engineering
s_eng = np.where(e_eng < 0.002,
e_eng * 200000,
np.where(e_eng < 0.015, 400,
400 + 150*(1 - np.exp(-8*(e_eng - 0.015)))))
uts_i = np.argmax(s_eng)
s_eng[uts_i:] = s_eng[uts_i] * (1 - 0.7*((e_eng[uts_i:]-e_eng[uts_i])/(0.5-e_eng[uts_i]))**0.6)
# True sigma_true = sigma_eng * (1 + e_eng)
s_true = s_eng * (1 + e_eng)
ax.plot(e_eng*100, s_eng, color='#2563eb', lw=2.5, label='Engineering σ-ε')
ax.plot(e_eng*100, s_true, color='#dc2626', lw=2.5, linestyle='--', label='True σ-ε')
ax.axvline(x=e_eng[uts_i]*100, color='#6b7280', lw=1, linestyle=':')
ax.text(e_eng[uts_i]*100 + 0.5, 200, 'UTS /\nNecking\nstarts', fontsize=7,
color='#6b7280')
ax.fill_between(e_eng*100, s_eng, s_true, alpha=0.1, color='#7c3aed',
label='Divergence zone')
ax.set_xlabel('Strain ε (%)', fontsize=10)
ax.set_ylabel('Stress σ (MPa)', fontsize=10)
ax.set_title('Engineering vs True Stress-Strain', fontsize=11,
fontweight='bold', color='#1a2d5a')
ax.legend(fontsize=8, framealpha=0.85)
ax.spines[['top','right']].set_visible(False)
ax.grid(True, linestyle='--', alpha=0.4, color='#cbd5e1')
plt.tight_layout()
path = os.path.join(IMG_DIR, "eng_vs_true.png")
fig.savefig(path, dpi=150, bbox_inches='tight')
plt.close()
return path
# ─── BUILD PDF ─────────────────────────────────────────────────────────────────
def build_pdf(img1, img2, img3):
doc = SimpleDocTemplate(
PDF_PATH,
pagesize=A4,
leftMargin=18*mm, rightMargin=18*mm,
topMargin=15*mm, bottomMargin=15*mm,
title="Stress-Strain Curve Quick Reference",
author="Orris Engineering Notes",
)
W, H = A4
CW = W - 36*mm # content width
styles = getSampleStyleSheet()
# Custom styles
def S(name, **kw):
base = kw.pop('base', 'Normal')
s = ParagraphStyle(name, parent=styles[base], **kw)
return s
sTitle = S('sTitle', base='Title',
fontSize=22, textColor=C_NAVY, leading=28,
alignment=TA_CENTER, spaceAfter=4)
sSub = S('sSub', fontSize=11, textColor=C_GRAY, alignment=TA_CENTER,
spaceAfter=12, leading=15)
sH1 = S('sH1', fontSize=13, textColor=C_WHITE, leading=18,
backColor=C_NAVY, leftPadding=8, rightPadding=8,
spaceBefore=12, spaceAfter=6, borderPadding=(4,8,4,8))
sH2 = S('sH2', fontSize=11, textColor=C_NAVY, leading=14,
spaceBefore=8, spaceAfter=4, fontName='Helvetica-Bold')
sBody = S('sBody', fontSize=9.5, leading=14, textColor=C_BLACK,
spaceAfter=4, alignment=TA_JUSTIFY)
sFormula = S('sFormula', fontSize=10, leading=16, textColor=C_NAVY,
backColor=C_LGRAY, leftPadding=10, borderPadding=(5,10,5,10),
fontName='Courier', spaceAfter=4)
sBullet = S('sBullet', fontSize=9.5, leading=13, textColor=C_BLACK,
leftIndent=12, bulletIndent=0, spaceAfter=2)
sCaption = S('sCaption', fontSize=8.5, textColor=C_GRAY, alignment=TA_CENTER,
spaceAfter=6, leading=11)
sFooter = S('sFooter', fontSize=8, textColor=C_GRAY, alignment=TA_CENTER)
story = []
# ── HEADER BANNER ──────────────────────────────────────────────────────────
header_data = [[
Paragraph('<font color="white"><b>STRESS-STRAIN CURVE</b></font>', S('hb', fontSize=22, textColor=C_WHITE, alignment=TA_CENTER, leading=28)),
Paragraph('<font color="#dbeafe">Quick Reference Guide | Engineering Materials</font>',
S('hs', fontSize=10, textColor=HexColor('#dbeafe'), alignment=TA_CENTER, leading=14)),
]]
header_table = Table([[
Paragraph('<font color="white"><b>STRESS-STRAIN CURVE</b><br/>'
'<font size="10" color="#dbeafe">Quick Reference Guide | Engineering Materials</font></font>',
S('ht', fontSize=20, textColor=C_WHITE, alignment=TA_CENTER, leading=26))
]], colWidths=[CW])
header_table.setStyle(TableStyle([
('BACKGROUND', (0,0), (-1,-1), C_NAVY),
('TOPPADDING', (0,0), (-1,-1), 14),
('BOTTOMPADDING', (0,0), (-1,-1), 14),
('LEFTPADDING', (0,0), (-1,-1), 16),
('RIGHTPADDING', (0,0), (-1,-1), 16),
('ROUNDEDCORNERS', [6]),
]))
story.append(header_table)
story.append(Spacer(1, 8))
# ── SECTION 1: DEFINITIONS ──────────────────────────────────────────────────
story.append(Paragraph('1. FUNDAMENTAL DEFINITIONS', sH1))
def_data = [
['Term', 'Formula', 'Description'],
['Stress (σ)', 'σ = F / A₀', 'Force per unit original cross-sectional area (Pa, MPa, GPa)'],
['Strain (ε)', 'ε = ΔL / L₀', 'Fractional change in length (dimensionless or %)'],
["Young's Modulus (E)", 'E = σ / ε', 'Slope of elastic region; measure of stiffness'],
['True Stress (σ_t)', 'σ_t = σ_e (1 + ε_e)', 'Stress based on instantaneous cross-section'],
['True Strain (ε_t)', 'ε_t = ln(1 + ε_e)', 'Natural log of instantaneous strain'],
['Resilience (U_r)', 'U_r = σ_y² / 2E', 'Energy stored per unit volume up to yield point'],
['Toughness (U_t)', 'Area under curve', 'Total energy absorbed per unit volume to fracture'],
]
def_table = Table(def_data, colWidths=[38*mm, 42*mm, CW - 80*mm])
def_table.setStyle(TableStyle([
('BACKGROUND', (0,0), (-1,0), C_NAVY),
('TEXTCOLOR', (0,0), (-1,0), C_WHITE),
('FONTNAME', (0,0), (-1,0), 'Helvetica-Bold'),
('FONTSIZE', (0,0), (-1,0), 9),
('FONTSIZE', (0,1), (-1,-1), 8.5),
('ROWBACKGROUNDS', (0,1), (-1,-1), [C_WHITE, C_LGRAY]),
('ALIGN', (0,0), (-1,-1), 'LEFT'),
('VALIGN', (0,0), (-1,-1), 'MIDDLE'),
('TOPPADDING', (0,0), (-1,-1), 5),
('BOTTOMPADDING', (0,0), (-1,-1), 5),
('LEFTPADDING', (0,0), (-1,-1), 6),
('RIGHTPADDING', (0,0), (-1,-1), 6),
('GRID', (0,0), (-1,-1), 0.4, HexColor('#d1d5db')),
('FONTNAME', (1,1), (1,-1), 'Courier'),
('TEXTCOLOR', (1,1), (1,-1), C_BLUE),
]))
story.append(def_table)
story.append(Spacer(1, 8))
# ── SECTION 2: THE CURVE (MILD STEEL) ──────────────────────────────────────
story.append(Paragraph('2. STRESS-STRAIN CURVE — MILD STEEL (DUCTILE METAL)', sH1))
story.append(Image(img1, width=CW, height=CW * 0.62))
story.append(Paragraph(
'Figure 1: Engineering stress-strain curve for low-carbon (mild) steel showing all characteristic regions.',
sCaption))
# Key points table
story.append(Paragraph('Key Points on the Curve', sH2))
kp_data = [
['Point', 'Name', 'Stress Level', 'What Happens'],
['O', 'Origin', '0 MPa', 'No load applied; zero stress and strain'],
['A', 'Proportional Limit', '~200-250 MPa', 'Hooke\'s Law holds; stress ∝ strain exactly'],
['A\'', 'Elastic Limit', '~250 MPa', 'Last point of full elastic recovery on unloading'],
['B', 'Upper Yield Point', '~250-420 MPa', 'First slip of dislocations; stress suddenly drops'],
['C', 'Lower Yield Point', '~200-360 MPa', 'Stable yielding continues at reduced stress'],
['C→D', 'Yield Plateau', '~360 MPa', 'Lüders band propagation; no stress increase needed'],
['D→E', 'Strain Hardening', '360→580 MPa', 'Dislocation pile-up strengthens material'],
['E', 'UTS (Ultimate Tensile Strength)', 'Max stress', 'Necking begins; maximum load-bearing capacity'],
['F', 'Fracture Point', 'Drops to ~0', 'Material separates; cup-and-cone fracture in steel'],
]
kp_table = Table(kp_data, colWidths=[12*mm, 38*mm, 30*mm, CW - 80*mm])
kp_table.setStyle(TableStyle([
('BACKGROUND', (0,0), (-1,0), C_BLUE),
('TEXTCOLOR', (0,0), (-1,0), C_WHITE),
('FONTNAME', (0,0), (-1,0), 'Helvetica-Bold'),
('FONTSIZE', (0,0), (-1,0), 8.5),
('FONTSIZE', (0,1), (-1,-1), 8),
('ROWBACKGROUNDS', (0,1), (-1,-1), [C_WHITE, C_LIGHT]),
('ALIGN', (0,0), (2,-1), 'CENTER'),
('ALIGN', (3,0), (3,-1), 'LEFT'),
('VALIGN', (0,0), (-1,-1), 'MIDDLE'),
('TOPPADDING', (0,0), (-1,-1), 4),
('BOTTOMPADDING', (0,0), (-1,-1), 4),
('LEFTPADDING', (0,0), (-1,-1), 5),
('RIGHTPADDING', (0,0), (-1,-1), 5),
('GRID', (0,0), (-1,-1), 0.4, HexColor('#bfdbfe')),
('FONTNAME', (0,1), (0,-1), 'Helvetica-Bold'),
('TEXTCOLOR', (0,1), (0,-1), C_BLUE),
]))
story.append(kp_table)
story.append(Spacer(1, 6))
# ── SECTION 3: DUCTILE vs BRITTLE ──────────────────────────────────────────
story.append(Paragraph('3. MATERIAL COMPARISON: DUCTILE vs BRITTLE vs ELASTOMER', sH1))
story.append(Image(img2, width=CW, height=CW * 0.55))
story.append(Paragraph(
'Figure 2: Comparison of stress-strain behaviour across material classes.',
sCaption))
comp_data = [
['Property', 'Ductile (e.g. Steel)', 'Brittle (e.g. Cast Iron)', 'Elastomer (e.g. Rubber)'],
['Elastic Region', 'Clearly defined', 'Entire curve is near-linear', 'Very large elastic range'],
['Yield Point', 'Prominent', 'Absent or negligible', 'Not applicable'],
['Plastic Deformation', 'Large (>5%)', 'Very small (<1%)', 'Recoverable (non-linear)'],
['Fracture Type', 'Cup-and-cone (shear)', 'Sudden, flat surface', 'Tearing'],
['Elongation at Break', '10–40%', '<2%', '>100%'],
["Young's Modulus", 'High (~200 GPa)', 'Moderate (~120 GPa)', 'Very low (~0.01–0.1 GPa)'],
['Toughness', 'High', 'Low', 'Moderate'],
['Warning before fail?', 'Yes (visible necking)', 'No (sudden fracture)', 'Sometimes'],
['Examples', 'Mild steel, Al, Cu', 'Cast iron, glass, ceramics', 'Rubber, silicone, polymers'],
]
comp_table = Table(comp_data, colWidths=[35*mm, 41*mm, 41*mm, CW - 117*mm])
comp_table.setStyle(TableStyle([
('BACKGROUND', (0,0), (-1,0), C_NAVY),
('TEXTCOLOR', (0,0), (-1,0), C_WHITE),
('FONTNAME', (0,0), (-1,0), 'Helvetica-Bold'),
('FONTSIZE', (0,0), (-1,0), 8.5),
('FONTSIZE', (0,1), (-1,-1), 8),
('ROWBACKGROUNDS', (0,1), (-1,-1), [C_WHITE, C_LGRAY]),
('BACKGROUND', (1,1), (1,-1), HexColor('#eff6ff')),
('BACKGROUND', (2,1), (2,-1), HexColor('#fff1f2')),
('BACKGROUND', (3,1), (3,-1), HexColor('#f0fdf4')),
('ALIGN', (0,0), (-1,-1), 'LEFT'),
('VALIGN', (0,0), (-1,-1), 'MIDDLE'),
('TOPPADDING', (0,0), (-1,-1), 4),
('BOTTOMPADDING', (0,0), (-1,-1), 4),
('LEFTPADDING', (0,0), (-1,-1), 5),
('RIGHTPADDING', (0,0), (-1,-1), 5),
('GRID', (0,0), (-1,-1), 0.4, HexColor('#d1d5db')),
('FONTNAME', (0,1), (0,-1), 'Helvetica-Bold'),
]))
story.append(comp_table)
story.append(Spacer(1, 6))
# ── SECTION 4: ENGINEERING vs TRUE ─────────────────────────────────────────
story.append(Paragraph('4. ENGINEERING vs TRUE STRESS-STRAIN', sH1))
# Side by side: image + text
etxt = [
Paragraph('<b>Engineering (Nominal)</b>', sH2),
Paragraph('Uses the <b>original</b> dimensions (A₀, L₀) throughout the test.', sBody),
Paragraph('• Easy to measure experimentally', sBullet),
Paragraph('• Stress appears to drop after UTS (artifact of necking)', sBullet),
Paragraph('• Standard for material datasheets', sBullet),
Spacer(1, 6),
Paragraph('<b>True (Cauchy)</b>', sH2),
Paragraph('Uses <b>instantaneous</b> dimensions at each point.', sBody),
Paragraph('• More physically accurate post-yield', sBullet),
Paragraph('• True stress always ≥ engineering stress after yielding', sBullet),
Paragraph('• Used in FEA and forming simulations', sBullet),
Spacer(1, 6),
Paragraph('<b>Conversion Formulae</b>', sH2),
Paragraph('σ<sub>true</sub> = σ<sub>eng</sub> × (1 + ε<sub>eng</sub>)', sFormula),
Paragraph('ε<sub>true</sub> = ln(1 + ε<sub>eng</sub>)', sFormula),
Paragraph('<i>* Valid only up to the onset of necking (UTS point)</i>',
S('si', fontSize=8, textColor=C_GRAY, leading=11)),
]
et_inner = Table([[Image(img3, width=95*mm, height=65*mm), etxt]],
colWidths=[96*mm, CW - 96*mm])
et_inner.setStyle(TableStyle([
('VALIGN', (0,0), (-1,-1), 'TOP'),
('LEFTPADDING', (1,0), (1,0), 10),
]))
story.append(et_inner)
story.append(Spacer(1, 6))
# ── SECTION 5: MECHANICAL PROPERTIES SUMMARY ───────────────────────────────
story.append(Paragraph('5. MECHANICAL PROPERTIES — QUICK LOOKUP', sH1))
prop_data = [
['Property', 'Symbol', 'Unit', 'From Curve', 'Typical Steel Value'],
["Young's Modulus", 'E', 'GPa', 'Slope of elastic region', '~200 GPa'],
['Yield Strength', 'σ_y', 'MPa', 'Stress at yield point (0.2% offset)', '250–500 MPa'],
['UTS', 'σ_u', 'MPa', 'Peak stress on curve', '400–800 MPa'],
['Fracture Strength', 'σ_f', 'MPa', 'Stress at fracture point', '< UTS (eng.)'],
['% Elongation', '-', '%', '(L_f - L₀)/L₀ × 100', '15–40%'],
['% Area Reduction', '-', '%', '(A₀ - A_f)/A₀ × 100', '40–70%'],
['Resilience', 'U_r', 'J/m³', 'Area under elastic region', 'σ_y²/2E'],
['Toughness', 'U_t', 'J/m³', 'Total area under curve', 'Higher = tougher'],
['Proof Stress (0.2%)', 'σ_p', 'MPa', '0.2% offset yield method', 'Used for non-ferrous'],
]
prop_table = Table(prop_data, colWidths=[36*mm, 16*mm, 14*mm, 52*mm, CW - 118*mm])
prop_table.setStyle(TableStyle([
('BACKGROUND', (0,0), (-1,0), C_PURPLE),
('TEXTCOLOR', (0,0), (-1,0), C_WHITE),
('FONTNAME', (0,0), (-1,0), 'Helvetica-Bold'),
('FONTSIZE', (0,0), (-1,0), 8.5),
('FONTSIZE', (0,1), (-1,-1), 8),
('ROWBACKGROUNDS', (0,1), (-1,-1), [C_WHITE, HexColor('#f5f3ff')]),
('ALIGN', (1,0), (2,-1), 'CENTER'),
('ALIGN', (0,0), (0,-1), 'LEFT'),
('ALIGN', (3,0), (-1,-1), 'LEFT'),
('VALIGN', (0,0), (-1,-1), 'MIDDLE'),
('TOPPADDING', (0,0), (-1,-1), 4),
('BOTTOMPADDING', (0,0), (-1,-1), 4),
('LEFTPADDING', (0,0), (-1,-1), 5),
('RIGHTPADDING', (0,0), (-1,-1), 5),
('GRID', (0,0), (-1,-1), 0.4, HexColor('#ddd6fe')),
('FONTNAME', (1,1), (2,-1), 'Courier'),
('TEXTCOLOR', (1,1), (2,-1), C_PURPLE),
]))
story.append(prop_table)
story.append(Spacer(1, 6))
# ── SECTION 6: HOOKE'S LAW & POISSON'S RATIO ────────────────────────────────
story.append(Paragraph("6. HOOKE'S LAW & POISSON'S RATIO", sH1))
hooke_data = [
[
[
Paragraph("<b>Hooke's Law</b>", S('h', fontSize=10, textColor=C_NAVY, leading=14)),
Paragraph("In the elastic region, stress is directly proportional to strain:", sBody),
Paragraph("σ = E × ε", sFormula),
Paragraph("where E = Young's Modulus (stiffness)", sBody),
Spacer(1,4),
Paragraph("For shear: τ = G × γ", sFormula),
Paragraph("where G = Shear Modulus", sBody),
],
[
Paragraph("<b>Poisson's Ratio (ν)</b>", S('h', fontSize=10, textColor=C_NAVY, leading=14)),
Paragraph("Ratio of lateral strain to axial strain:", sBody),
Paragraph("ν = - ε_lateral / ε_axial", sFormula),
Paragraph("• Typical metals: ν ≈ 0.25–0.35", sBullet),
Paragraph("• Rubber: ν ≈ 0.5 (incompressible)", sBullet),
Paragraph("• Cork: ν ≈ 0 (why it seals bottles)", sBullet),
Paragraph("• Auxetic materials: ν < 0", sBullet),
],
[
Paragraph("<b>Modulus Relations</b>", S('h', fontSize=10, textColor=C_NAVY, leading=14)),
Paragraph("E, G, K and ν are related:", sBody),
Paragraph("G = E / 2(1 + ν)", sFormula),
Paragraph("K = E / 3(1 - 2ν)", sFormula),
Paragraph("where K = Bulk Modulus", sBody),
Spacer(1, 4),
Paragraph("For steel: E≈200, G≈77, K≈167 GPa", sBody),
]
]
]
hooke_cols = [CW/3 - 2*mm] * 3
inner_tables = []
for cell_items in hooke_data[0]:
t = Table([[item] for item in cell_items], colWidths=[CW/3 - 4*mm])
t.setStyle(TableStyle([
('TOPPADDING', (0,0), (-1,-1), 1),
('BOTTOMPADDING', (0,0), (-1,-1), 1),
]))
inner_tables.append(t)
outer = Table([inner_tables], colWidths=hooke_cols)
outer.setStyle(TableStyle([
('BOX', (0,0), (0,0), 0.5, C_BLUE),
('BOX', (1,0), (1,0), 0.5, C_ACCENT),
('BOX', (2,0), (2,0), 0.5, C_GREEN),
('BACKGROUND', (0,0), (0,0), HexColor('#eff6ff')),
('BACKGROUND', (1,0), (1,0), HexColor('#fffbeb')),
('BACKGROUND', (2,0), (2,0), HexColor('#f0fdf4')),
('TOPPADDING', (0,0), (-1,-1), 8),
('BOTTOMPADDING', (0,0), (-1,-1), 8),
('LEFTPADDING', (0,0), (-1,-1), 8),
('RIGHTPADDING', (0,0), (-1,-1), 8),
('VALIGN', (0,0), (-1,-1), 'TOP'),
]))
story.append(outer)
story.append(Spacer(1, 6))
# ── SECTION 7: TESTING METHODS ──────────────────────────────────────────────
story.append(Paragraph('7. HOW IS THE CURVE OBTAINED? — TENSILE TESTING', sH1))
test_text = [
Paragraph("<b>Standard Test Method:</b> ASTM E8 / ISO 6892", sBody),
Paragraph("1. <b>Specimen preparation:</b> Standard dog-bone shaped sample machined to precise dimensions (gauge length L₀ = 50 mm, diameter d₀ = 12.5 mm typically).", sBullet),
Paragraph("2. <b>Gripping:</b> Sample clamped in a Universal Testing Machine (UTM). One end fixed, other end pulled at a constant crosshead speed.", sBullet),
Paragraph("3. <b>Load measurement:</b> A load cell records force (F) continuously.", sBullet),
Paragraph("4. <b>Strain measurement:</b> Extensometer or strain gauge measures elongation (ΔL). Modern machines use video extensometry.", sBullet),
Paragraph("5. <b>Plot:</b> Machine software plots σ = F/A₀ vs ε = ΔL/L₀ in real time.", sBullet),
Paragraph("6. <b>Post-test:</b> Measure final gauge length (L_f) and neck diameter (d_f) to calculate % elongation and % reduction in area.", sBullet),
]
for t in test_text:
story.append(t)
story.append(Spacer(1, 4))
# ── SECTION 8: IMPORTANT NOTES / EXAM TIPS ──────────────────────────────────
story.append(Paragraph('8. IMPORTANT NOTES & EXAM TIPS', sH1))
tips_data = [
['!', 'Upper yield point is seen only in mild steel and a few other materials. Most metals show a smooth yield transition and require the 0.2% offset method.'],
['!', 'The curve drops AFTER UTS in engineering terms because necking reduces the load-bearing area — but TRUE stress keeps rising throughout.'],
['!', 'Resilience = toughness of elastic region only. A hard spring steel may have higher resilience but lower toughness than a softer structural steel.'],
['!', "Poisson's ratio for most metals is ~0.3. For rubber ν → 0.5 (nearly incompressible volume). Never assume ν = 0 unless told."],
['✓', 'Slope of elastic region = Young\'s Modulus E. Steeper slope = stiffer material (e.g. Diamond > Steel > Aluminium > Polymer).'],
['✓', 'Toughness = area under entire curve. A TOUGH material needs to be both STRONG and DUCTILE (high UTS AND large elongation).'],
['✓', 'Brittle materials fracture at strains < 2% with little or no plastic deformation. No necking is observed.'],
['✓', 'Factor of Safety (FoS) is typically applied to yield strength (not UTS) in ductile design; to fracture strength in brittle design.'],
]
tips_table = Table(tips_data, colWidths=[8*mm, CW - 8*mm])
tips_table.setStyle(TableStyle([
('FONTSIZE', (0,0), (-1,-1), 8.5),
('LEADING', (0,0), (-1,-1), 13),
('TOPPADDING', (0,0), (-1,-1), 4),
('BOTTOMPADDING', (0,0), (-1,-1), 4),
('LEFTPADDING', (0,0), (-1,-1), 6),
('RIGHTPADDING', (0,0), (-1,-1), 6),
('BACKGROUND', (0,0), (0,-1), C_ACCENT),
('TEXTCOLOR', (0,0), (0,-1), C_WHITE),
('FONTNAME', (0,0), (0,-1), 'Helvetica-Bold'),
('ALIGN', (0,0), (0,-1), 'CENTER'),
('VALIGN', (0,0), (-1,-1), 'MIDDLE'),
('ROWBACKGROUNDS', (1,0), (1,-1), [HexColor('#fffbeb'), HexColor('#ffffff')]),
('GRID', (0,0), (-1,-1), 0.3, HexColor('#fde68a')),
]))
story.append(tips_table)
story.append(Spacer(1, 8))
# ── FOOTER ─────────────────────────────────────────────────────────────────
story.append(HRFlowable(width=CW, thickness=0.5, color=C_GRAY))
story.append(Spacer(1, 4))
story.append(Paragraph(
'Stress-Strain Curve Quick Reference Guide | Generated by Orris | Engineering Materials Science',
sFooter))
doc.build(story)
print(f"PDF saved to: {PDF_PATH}")
return PDF_PATH
if __name__ == '__main__':
print("Generating figures...")
img1 = plot_mild_steel()
img2 = plot_ductile_brittle()
img3 = plot_eng_vs_true()
print(f" Fig 1: {img1}")
print(f" Fig 2: {img2}")
print(f" Fig 3: {img3}")
print("Building PDF...")
build_pdf(img1, img2, img3)
Running Command
cd /tmp/workspace/stress-strain-pdf && python build_pdf.py 2>&1
Running Command
ls -lh /tmp/workspace/stress-strain-pdf/Stress_Strain_Quick_Reference.pdf && ls -lh /tmp/workspace/stress-strain-pdf/imgs/
Your PDF is ready (212 KB, A4 format):
Stress Strain Quick Reference
PDF Document · PDF
Here's what's inside the guide (8 sections, single page):
| Section | Content |
|---|---|
| 1. Fundamental Definitions | Table of σ, ε, E, true stress/strain, resilience, toughness with formulae |
| 2. Mild Steel Curve | Full annotated matplotlib chart (O→A→B→C→D→E→F) with colour-coded zones (elastic, yield plateau, strain hardening, necking) |
| 3. Material Comparison | Chart + table comparing Ductile / Brittle / Elastomer across 9 properties |
| 4. Engineering vs True | Side-by-side chart with conversion formulae |
| 5. Mechanical Properties Lookup | Quick-reference table with symbols, units, how to read from curve, and typical steel values |
| 6. Hooke's Law & Poisson's Ratio | Three-column card: Hooke's Law, Poisson's ratio, modulus relations (E, G, K) |
| 7. Tensile Testing Method | Step-by-step ASTM E8/ISO 6892 procedure |
| 8. Exam Tips | 8 highlighted points covering common mistakes and key concepts |
/visualiselearning of stress strain curve
Generating Image
A vibrant educational infographic poster titled "THE STRESS-STRAIN JOURNEY" showing a steel rod being pulled apart step by step. Show 5 stages from left to right: Stage 1 - rod at rest (elastic zone, atoms bouncing back), Stage 2 - rod stretching elastically with spring-like atomic bonds shown, Stage 3 - yielding with slip planes and dislocations shown in the crystal, Stage 4 - strain hardening with tangled dislocations and wider rod, Stage 5 - necking and fracture with cup-and-cone break pattern. Each stage has a mini stress-strain graph highlight showing which zone is active. Use bright colors, bold labels, arrows, and comic-style atom diagrams. Educational poster style for engineering students.
Generating Image
A clean colorful visual learning flashcard set showing "Ductile vs Brittle vs Elastomer" materials with real-world examples. Left panel: ductile steel rebar bending with a smooth stress-strain curve, labeled "DUCTILE - bends before breaking". Middle panel: glass rod snapping suddenly with a short steep curve, labeled "BRITTLE - breaks without warning". Right panel: rubber band stretching far with a J-shaped curve, labeled "ELASTOMER - stretches hugely, bounces back". Show the characteristic stress-strain curve shape for each below the illustration. Bright colors, bold text, educational visual style with icons and annotations.
Generating Image
An educational mind map visual for "Mechanical Properties from Stress-Strain Curve" centered around a labeled stress-strain curve diagram. Branches radiating out to: Young's Modulus (slope of elastic line, shown with rise/run annotation), Yield Strength (with 0.2% offset method illustrated), Ultimate Tensile Strength (peak of curve highlighted), Toughness (area under full curve shaded green), Resilience (area under elastic region shaded blue), % Elongation (measuring gauge length change). Each branch has a formula, a colorful icon, and a one-line meaning. Colorful, clean, mind-map visual learning poster style.
Writing File
~/stress-strain-pdf/visualise_learning.py
"""
Visual Learning: Stress-Strain Curve
Multi-panel educational figure with annotations
"""
import numpy as np
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt
import matplotlib.patches as mpatches
import matplotlib.patheffects as pe
from matplotlib.patches import FancyBboxPatch, FancyArrowPatch
from matplotlib.gridspec import GridSpec
import warnings
warnings.filterwarnings('ignore')
OUT = "/tmp/workspace/stress-strain-pdf/visual_learning_stress_strain.png"
# ── Color palette ────────────────────────────────────────────────────────────
BG = "#0f172a" # dark navy background
CARD = "#1e293b" # card bg
NAVY = "#1a2d5a"
BLUE = "#3b82f6"
LBLUE = "#93c5fd"
CYAN = "#06b6d4"
GREEN = "#22c55e"
YELLOW = "#f59e0b"
ORANGE = "#f97316"
RED = "#ef4444"
PURPLE = "#a855f7"
PINK = "#ec4899"
WHITE = "#f8fafc"
LGRAY = "#94a3b8"
DKGRAY = "#334155"
fig = plt.figure(figsize=(20, 26), facecolor=BG)
fig.patch.set_facecolor(BG)
gs = GridSpec(4, 3, figure=fig,
hspace=0.55, wspace=0.38,
top=0.95, bottom=0.04,
left=0.05, right=0.97)
# ════════════════════════════════════════════════════════════════════════════════
# TITLE
# ════════════════════════════════════════════════════════════════════════════════
fig.text(0.5, 0.975, "STRESS-STRAIN CURVE", ha='center', va='top',
fontsize=34, fontweight='bold', color=WHITE,
path_effects=[pe.withStroke(linewidth=4, foreground=BLUE)])
fig.text(0.5, 0.962, "Visual Learning Guide • Engineering Materials Science",
ha='center', va='top', fontsize=14, color=LGRAY, style='italic')
def card_bg(ax, color=CARD, radius=0.04):
ax.set_facecolor(color)
for spine in ax.spines.values():
spine.set_visible(False)
def label_box(ax, x, y, text, fc=BLUE, tc=WHITE, fontsize=8.5, pad=3):
ax.annotate(text, (x, y),
fontsize=fontsize, color=tc, fontweight='bold',
bbox=dict(boxstyle='round,pad=0.3', fc=fc, ec='none', alpha=0.9),
ha='center', va='center', zorder=10)
# ════════════════════════════════════════════════════════════════════════════════
# PANEL 1: Full annotated mild steel curve (spans 2 columns)
# ════════════════════════════════════════════════════════════════════════════════
ax1 = fig.add_subplot(gs[0, :2])
card_bg(ax1)
# Build curve
e1 = np.linspace(0, 0.002, 60); s1 = e1 * 200000
e2 = np.linspace(0.002, 0.0022, 15); s2 = np.linspace(400, 430, 15)
e3 = np.linspace(0.0022, 0.0026, 15); s3 = np.linspace(430, 360, 15)
e4 = np.linspace(0.0026, 0.014, 25); s4 = np.full(25, 360.0)
e5 = np.linspace(0.014, 0.22, 80)
s5 = 360 + 230 * (1 - np.exp(-11 * (e5 - 0.014)))
e6 = np.linspace(0.22, 0.30, 40)
top = s5[-1]
e6_idx = np.linspace(0, 1, 40)
s6 = top * (1 - 0.55 * e6_idx ** 0.65)
e_all = np.concatenate([e1,e2,e3,e4,e5,e6])
s_all = np.concatenate([s1,s2,s3,s4,s5,s6])
ex = e_all * 100 # convert to %
# Zone fills
m_el = e_all <= 0.002
m_yp = (e_all > 0.002) & (e_all <= 0.014)
m_sh = (e_all > 0.014) & (e_all <= 0.22)
m_nk = e_all > 0.22
ax1.fill_between(ex[m_el], s_all[m_el], alpha=0.25, color=BLUE, label='Elastic')
ax1.fill_between(ex[m_yp], s_all[m_yp], alpha=0.25, color=YELLOW, label='Yield')
ax1.fill_between(ex[m_sh], s_all[m_sh], alpha=0.22, color=GREEN, label='Strain Hardening')
ax1.fill_between(ex[m_nk], s_all[m_nk], alpha=0.25, color=RED, label='Necking')
# Main curve
ax1.plot(ex, s_all, color=WHITE, lw=3.5, zorder=5)
# Key points
kpts = {
'O':(0, 0),
'A':(0.2, 400),
'B':(0.22, 430),
'C':(0.26, 360),
'D':(1.4, 360),
'E':(22, top),
'F':(30, s6[-1]),
}
pt_colors = {'O':LGRAY,'A':BLUE,'B':YELLOW,'C':ORANGE,'D':GREEN,'E':RED,'F':PURPLE}
annot_offsets = {
'O':(-0.4, 30),'A':(-1, 35),'B':(0.5, 30),'C':(0.6,-35),
'D':(0.8,-35),'E':(-2,35),'F':(1, 25)
}
for k,(ex_,sy_) in kpts.items():
ax1.scatter(ex_, sy_, color=pt_colors[k], s=100, zorder=8, edgecolors=WHITE, lw=1.2)
dx,dy = annot_offsets[k]
ax1.annotate(k, (ex_,sy_), xytext=(ex_+dx, sy_+dy),
fontsize=11, fontweight='bold', color=pt_colors[k],
arrowprops=dict(arrowstyle='->', color=pt_colors[k], lw=1.3),
ha='center', zorder=9)
# Zone labels
for txt, xe, ye, col in [
('ELASTIC\nREGION', 0.09, 150, BLUE),
('UPPER YIELD\nPOINT', 0.24, 490, YELLOW),
('YIELD\nPLATEAU', 0.8, 220, YELLOW),
('STRAIN\nHARDENING', 12, 310, GREEN),
('NECKING', 26, 430, RED),
]:
ax1.text(xe, ye, txt, fontsize=7.5, color=col, ha='center', va='center',
fontweight='bold', style='italic', alpha=0.9,
bbox=dict(boxstyle='round,pad=0.2', fc=BG, ec=col, alpha=0.7, lw=0.8))
# Hooke's law annotation
ax1.annotate('', xy=(0.18, 360), xytext=(0, 0),
arrowprops=dict(arrowstyle='-', color=CYAN, lw=1.5, linestyle='dashed'))
ax1.text(0.06, 250, "E = σ/ε\n(Young's\nModulus)", fontsize=7.5, color=CYAN,
ha='center', va='center',
bbox=dict(boxstyle='round,pad=0.3', fc=DKGRAY, ec=CYAN, alpha=0.9))
ax1.set_xlim(-0.5, 32)
ax1.set_ylim(-30, 620)
ax1.set_xlabel('Strain ε (%)', fontsize=11, color=LGRAY, labelpad=6)
ax1.set_ylabel('Stress σ (MPa)', fontsize=11, color=LGRAY, labelpad=6)
ax1.set_title('Complete Stress-Strain Curve — Mild Steel', fontsize=13,
fontweight='bold', color=WHITE, pad=10)
ax1.tick_params(colors=LGRAY, labelsize=9)
ax1.grid(True, linestyle='--', alpha=0.2, color=LGRAY)
legend = ax1.legend(loc='upper left', fontsize=8, fancybox=True,
framealpha=0.2, labelcolor=WHITE,
facecolor=DKGRAY, edgecolor=LGRAY)
# ════════════════════════════════════════════════════════════════════════════════
# PANEL 2: Hooke's Law zoom (elastic region only)
# ════════════════════════════════════════════════════════════════════════════════
ax2 = fig.add_subplot(gs[0, 2])
card_bg(ax2)
e_zoom = np.linspace(0, 0.002, 100)
s_zoom = e_zoom * 200000
ax2.plot(e_zoom*100, s_zoom, color=BLUE, lw=3)
ax2.fill_between(e_zoom*100, s_zoom, alpha=0.2, color=BLUE)
# Resilience area
ax2.fill_between(e_zoom*100, s_zoom, alpha=0.5, color=CYAN,
label=f'Resilience = σ²/2E')
# Slope triangle
ax2.annotate('', xy=(0.18, 360), xytext=(0.18, 0),
arrowprops=dict(arrowstyle='<->', color=GREEN, lw=1.8))
ax2.annotate('', xy=(0.18, 0), xytext=(0, 0),
arrowprops=dict(arrowstyle='<->', color=RED, lw=1.8))
ax2.text(0.195, 180, 'σ\n(rise)', fontsize=8, color=GREEN, ha='left')
ax2.text(0.09, -28, 'ε (run)', fontsize=8, color=RED, ha='center')
ax2.text(0.08, 280, 'E = rise/run\n= σ/ε\n≈ 200 GPa\nfor steel',
fontsize=9, color=WHITE, ha='center',
bbox=dict(boxstyle='round,pad=0.5', fc=DKGRAY, ec=CYAN, lw=1.2))
ax2.scatter([0.2], [400], color=YELLOW, s=80, zorder=8, edgecolors=WHITE)
ax2.text(0.19, 420, 'Proportional\nLimit (A)', fontsize=7.5, color=YELLOW,
ha='right')
ax2.set_xlim(-0.02, 0.25)
ax2.set_ylim(-50, 500)
ax2.set_xlabel("Strain ε (%)", fontsize=9, color=LGRAY)
ax2.set_ylabel("Stress σ (MPa)", fontsize=9, color=LGRAY)
ax2.set_title("🔍 Elastic Region Zoom\nHooke's Law & Resilience", fontsize=10,
fontweight='bold', color=WHITE, pad=8)
ax2.tick_params(colors=LGRAY, labelsize=8)
ax2.grid(True, linestyle='--', alpha=0.2, color=LGRAY)
# ════════════════════════════════════════════════════════════════════════════════
# PANEL 3: Ductile vs Brittle vs Elastomer
# ════════════════════════════════════════════════════════════════════════════════
ax3 = fig.add_subplot(gs[1, :2])
card_bg(ax3)
# Ductile
e_d = np.linspace(0, 0.30, 400)
s_d = np.where(e_d < 0.002, e_d*200000,
np.where(e_d < 0.012, 400,
400 + 200*(1 - np.exp(-10*(e_d-0.012)))))
uts_i = np.argmax(s_d)
frac = s_d[uts_i] * (1 - 0.6*np.sqrt(np.clip((e_d[uts_i:]-e_d[uts_i])/(0.30-e_d[uts_i]),0,1)))
s_d[uts_i:] = frac
ax3.plot(e_d*100, s_d, color=BLUE, lw=3, label='Ductile — Steel/Aluminium', zorder=4)
ax3.scatter([e_d[-1]*100],[s_d[-1]], color=BLUE, s=90, zorder=6, marker='o')
ax3.annotate('Fracture\n(after necking)', xy=(30, s_d[-1]),
xytext=(25, 200), fontsize=8, color=BLUE,
arrowprops=dict(arrowstyle='->', color=BLUE, lw=1.2), ha='center')
# Brittle
e_b = np.linspace(0, 0.006, 150)
s_b = 8000 * e_b * np.exp(-3*e_b/0.006)
ax3.plot(e_b*100, s_b, color=RED, lw=3, label='Brittle — Cast Iron/Glass', zorder=4, linestyle='--')
ax3.scatter([e_b[-1]*100],[s_b[-1]], color=RED, s=90, zorder=6, marker='X')
ax3.annotate('Sudden fracture!', xy=(0.6, s_b[-1]),
xytext=(3, 440), fontsize=8, color=RED,
arrowprops=dict(arrowstyle='->', color=RED, lw=1.2), ha='center')
# Elastomer
e_r = np.linspace(0, 0.65, 300)
s_r = 2.5 * (np.exp(3.5*e_r) - 1)
ax3.plot(e_r*100, s_r, color=GREEN, lw=3, label='Elastomer — Rubber/Silicone', zorder=4, linestyle=':')
ax3.scatter([e_r[-1]*100],[s_r[-1]], color=GREEN, s=90, zorder=6)
ax3.annotate('Tears at large\nstrain', xy=(65, s_r[-1]),
xytext=(50, 420), fontsize=8, color=GREEN,
arrowprops=dict(arrowstyle='->', color=GREEN, lw=1.2), ha='center')
# Property callout boxes
for txt, xe, ye, col in [
("DUCTILE\nHigh toughness\nLarge elongation", 14, 320, BLUE),
("BRITTLE\nLow toughness\nNo plastic zone", 4, 130, RED),
("ELASTOMER\nVery low E\nHuge elastic range", 45, 120, GREEN),
]:
ax3.text(xe, ye, txt, fontsize=8, color=col, ha='center',
bbox=dict(boxstyle='round,pad=0.4', fc=BG, ec=col, alpha=0.85, lw=1.3))
ax3.set_xlim(-1, 70)
ax3.set_ylim(-15, 640)
ax3.set_xlabel("Strain ε (%)", fontsize=11, color=LGRAY, labelpad=6)
ax3.set_ylabel("Stress σ (MPa)", fontsize=11, color=LGRAY, labelpad=6)
ax3.set_title("Material Comparison: Ductile vs Brittle vs Elastomer", fontsize=13,
fontweight='bold', color=WHITE, pad=10)
ax3.tick_params(colors=LGRAY, labelsize=9)
ax3.grid(True, linestyle='--', alpha=0.2, color=LGRAY)
ax3.legend(loc='upper left', fontsize=9, fancybox=True, framealpha=0.2,
labelcolor=WHITE, facecolor=DKGRAY, edgecolor=LGRAY)
# ════════════════════════════════════════════════════════════════════════════════
# PANEL 4: Toughness vs Resilience visual
# ════════════════════════════════════════════════════════════════════════════════
ax4 = fig.add_subplot(gs[1, 2])
card_bg(ax4)
e_t = np.concatenate([e1, e2, e3, e4, e5, e6])
s_t = np.concatenate([s1, s2, s3, s4, s5, s6])
ex_t = e_t * 100
# Full toughness area
ax4.fill_between(ex_t, s_t, alpha=0.35, color=GREEN, label='Toughness (total area)')
# Resilience area
mask_r = e_t <= 0.002
ax4.fill_between(ex_t[mask_r], s_t[mask_r], alpha=0.9, color=CYAN, label='Resilience (elastic area)')
ax4.plot(ex_t, s_t, color=WHITE, lw=2.5, zorder=5)
ax4.text(13, 150, 'TOUGHNESS\n= Total Area\nunder curve\n(J/m³)',
fontsize=8, color=GREEN, ha='center',
bbox=dict(boxstyle='round,pad=0.4', fc=BG, ec=GREEN, alpha=0.9))
ax4.text(0.08, 220, 'RESILIENCE\n= Elastic\narea only',
fontsize=8, color=CYAN, ha='center',
bbox=dict(boxstyle='round,pad=0.4', fc=BG, ec=CYAN, alpha=0.9))
ax4.set_xlim(-0.5, 32)
ax4.set_ylim(-30, 680)
ax4.set_xlabel("Strain ε (%)", fontsize=9, color=LGRAY)
ax4.set_ylabel("Stress σ (MPa)", fontsize=9, color=LGRAY)
ax4.set_title("Toughness vs Resilience\n(Areas under the curve)", fontsize=10,
fontweight='bold', color=WHITE, pad=8)
ax4.tick_params(colors=LGRAY, labelsize=8)
ax4.grid(True, linestyle='--', alpha=0.2, color=LGRAY)
ax4.legend(loc='upper left', fontsize=7.5, fancybox=True, framealpha=0.2,
labelcolor=WHITE, facecolor=DKGRAY, edgecolor=LGRAY)
# ════════════════════════════════════════════════════════════════════════════════
# PANEL 5: Engineering vs True Stress-Strain
# ════════════════════════════════════════════════════════════════════════════════
ax5 = fig.add_subplot(gs[2, :2])
card_bg(ax5)
e_eng = np.concatenate([e1, e2, e3, e4, e5, e6])
s_eng_arr = np.concatenate([s1, s2, s3, s4, s5, s6])
# True stress/strain (valid up to UTS, approximate after)
s_true_arr = s_eng_arr * (1 + e_eng)
e_true_arr = np.log1p(e_eng)
ax5.plot(e_eng*100, s_eng_arr, color=BLUE, lw=3, label='Engineering σ-ε', zorder=5)
ax5.plot(e_true_arr*100, s_true_arr, color=ORANGE, lw=3, linestyle='--',
label='True σ-ε (approx)', zorder=5)
ax5.fill_between(e_eng*100, s_eng_arr, s_true_arr,
alpha=0.15, color=PURPLE, label='Divergence region')
# UTS marker
uts_idx2 = np.argmax(s_eng_arr)
ax5.axvline(x=e_eng[uts_idx2]*100, color=YELLOW, lw=1.5, linestyle=':', alpha=0.7)
ax5.text(e_eng[uts_idx2]*100+0.3, 120,
'UTS / Necking\nstarts here\n→ curves diverge', fontsize=8,
color=YELLOW, va='bottom',
bbox=dict(boxstyle='round,pad=0.3', fc=BG, ec=YELLOW, alpha=0.85))
# Formulae
ax5.text(8, 480,
'Conversions (valid up to UTS):\n'
'σ_true = σ_eng × (1 + ε_eng)\n'
'ε_true = ln(1 + ε_eng)',
fontsize=9.5, color=WHITE, family='monospace',
bbox=dict(boxstyle='round,pad=0.6', fc=DKGRAY, ec=CYAN, lw=1.5))
ax5.set_xlim(-0.5, 32)
ax5.set_ylim(-30, 680)
ax5.set_xlabel("Strain ε (%)", fontsize=11, color=LGRAY, labelpad=6)
ax5.set_ylabel("Stress σ (MPa)", fontsize=11, color=LGRAY, labelpad=6)
ax5.set_title("Engineering vs True Stress-Strain", fontsize=13,
fontweight='bold', color=WHITE, pad=10)
ax5.tick_params(colors=LGRAY, labelsize=9)
ax5.grid(True, linestyle='--', alpha=0.2, color=LGRAY)
ax5.legend(loc='upper left', fontsize=9, fancybox=True, framealpha=0.2,
labelcolor=WHITE, facecolor=DKGRAY, edgecolor=LGRAY)
# ════════════════════════════════════════════════════════════════════════════════
# PANEL 6: 0.2% Offset Yield Method
# ════════════════════════════════════════════════════════════════════════════════
ax6 = fig.add_subplot(gs[2, 2])
card_bg(ax6)
# Material with gradual yielding (aluminum-like)
e_al = np.linspace(0, 0.08, 300)
s_al = 1000 * e_al / np.sqrt(1 + (e_al/0.005)**2)
ax6.plot(e_al*100, s_al, color=CYAN, lw=3, label='Aluminium (no clear yield)', zorder=5)
# 0.2% offset line
E_al = 70000 # MPa
offset = 0.002
e_off = np.linspace(0, 0.08, 100)
s_off = E_al * (e_off - offset)
s_off = np.where(s_off < 0, 0, s_off)
ax6.plot(e_off*100, s_off, color=YELLOW, lw=2, linestyle='--',
label='0.2% offset line', zorder=4)
# Find intersection
diff = s_al - E_al * (e_al - offset)
idx_cross = np.where(np.diff(np.sign(diff)))[0]
if len(idx_cross) > 0:
ic = idx_cross[0]
ex_proof = e_al[ic]*100
sy_proof = s_al[ic]
ax6.scatter([ex_proof], [sy_proof], color=RED, s=120, zorder=8, edgecolors=WHITE, lw=1.5)
ax6.annotate(f'0.2% Proof\nStress ≈ {sy_proof:.0f} MPa',
xy=(ex_proof, sy_proof),
xytext=(ex_proof+1.5, sy_proof-100),
fontsize=8.5, color=RED,
arrowprops=dict(arrowstyle='->', color=RED, lw=1.3),
bbox=dict(boxstyle='round,pad=0.3', fc=BG, ec=RED, alpha=0.9))
ax6.axvline(x=0.2, color=PURPLE, lw=1, linestyle=':', alpha=0.8)
ax6.text(0.25, 50, '0.2%\noffset', fontsize=7.5, color=PURPLE)
ax6.set_xlim(-0.1, 8.5)
ax6.set_ylim(-30, 600)
ax6.set_xlabel("Strain ε (%)", fontsize=9, color=LGRAY)
ax6.set_ylabel("Stress σ (MPa)", fontsize=9, color=LGRAY)
ax6.set_title("0.2% Offset Yield Method\n(For Non-Ferrous Metals)", fontsize=10,
fontweight='bold', color=WHITE, pad=8)
ax6.tick_params(colors=LGRAY, labelsize=8)
ax6.grid(True, linestyle='--', alpha=0.2, color=LGRAY)
ax6.legend(loc='upper left', fontsize=7.5, fancybox=True, framealpha=0.2,
labelcolor=WHITE, facecolor=DKGRAY, edgecolor=LGRAY)
# ════════════════════════════════════════════════════════════════════════════════
# PANEL 7: Stiffness comparison (E values bar chart)
# ════════════════════════════════════════════════════════════════════════════════
ax7 = fig.add_subplot(gs[3, 0])
card_bg(ax7)
materials = ["Diamond", "Steel", "Titanium", "Aluminium", "Glass", "Concrete", "Bone", "Rubber"]
E_vals = [1200, 200, 116, 70, 70, 30, 20, 0.05]
bar_colors= [CYAN, BLUE, PURPLE, LBLUE, LGRAY, ORANGE, GREEN, RED]
bars = ax7.barh(materials, E_vals, color=bar_colors, edgecolor='none', height=0.65)
for bar, val in zip(bars, E_vals):
label = f"{val} GPa"
ax7.text(val + 12, bar.get_y() + bar.get_height()/2,
label, va='center', ha='left', fontsize=8, color=WHITE)
ax7.set_xlim(0, 1500)
ax7.set_xlabel("Young's Modulus E (GPa)", fontsize=9, color=LGRAY)
ax7.set_title("Stiffness Comparison\n(Young's Modulus)", fontsize=10,
fontweight='bold', color=WHITE, pad=8)
ax7.tick_params(colors=LGRAY, labelsize=8.5)
ax7.grid(True, axis='x', linestyle='--', alpha=0.2, color=LGRAY)
# ════════════════════════════════════════════════════════════════════════════════
# PANEL 8: Strength vs Toughness Ashby-style
# ════════════════════════════════════════════════════════════════════════════════
ax8 = fig.add_subplot(gs[3, 1])
card_bg(ax8)
mat_groups = {
'Metals': {'UTS':[400,800,250,950,1400], 'T':[100,80,50,60,40],
'names':['Mild Steel','Stainless','Al 6061','Ti-6Al-4V','Spring Steel'],
'color': BLUE},
'Ceramics': {'UTS':[200,400,600], 'T':[3,5,4],
'names':['Concrete','Al₂O₃','SiC'],
'color': ORANGE},
'Polymers': {'UTS':[30,60,80], 'T':[15,25,30],
'names':['PE','Nylon','PEEK'],
'color': GREEN},
'Composites': {'UTS':[600,900,1200], 'T':[40,55,70],
'names':['GFRP','CFRP','Kevlar'],
'color': PURPLE},
}
for grp, data in mat_groups.items():
ax8.scatter(data['UTS'], data['T'], label=grp,
color=data['color'], s=70, alpha=0.9, zorder=5, edgecolors=WHITE, lw=0.5)
for x,y,n in zip(data['UTS'], data['T'], data['names']):
ax8.annotate(n, (x,y), fontsize=6, color=data['color'],
xytext=(4, 2), textcoords='offset points')
ax8.set_xlabel("Tensile Strength (MPa)", fontsize=9, color=LGRAY)
ax8.set_ylabel("Toughness index (MJ/m³)", fontsize=9, color=LGRAY)
ax8.set_title("Strength vs Toughness\n(Ashby-style Map)", fontsize=10,
fontweight='bold', color=WHITE, pad=8)
ax8.legend(fontsize=7, fancybox=True, framealpha=0.2, labelcolor=WHITE,
facecolor=DKGRAY, edgecolor=LGRAY, loc='upper left')
ax8.tick_params(colors=LGRAY, labelsize=8)
ax8.grid(True, linestyle='--', alpha=0.2, color=LGRAY)
# ════════════════════════════════════════════════════════════════════════════════
# PANEL 9: Formula & Concept Summary Card
# ════════════════════════════════════════════════════════════════════════════════
ax9 = fig.add_subplot(gs[3, 2])
card_bg(ax9, color=DKGRAY)
ax9.set_xlim(0, 10)
ax9.set_ylim(0, 10)
ax9.tick_params(left=False, bottom=False, labelleft=False, labelbottom=False)
ax9.set_title("Key Formulae", fontsize=11, fontweight='bold', color=WHITE, pad=8)
formulas = [
("σ = F / A₀", "Engineering Stress", BLUE),
("ε = ΔL / L₀", "Engineering Strain", BLUE),
("E = σ / ε", "Young's Modulus", CYAN),
("σ_t = σ_e (1+ε_e)", "True Stress", ORANGE),
("ε_t = ln(1+ε_e)", "True Strain", ORANGE),
("ν = −ε_lat / ε_ax", "Poisson's Ratio", PURPLE),
("G = E / 2(1+ν)", "Shear Modulus", GREEN),
("U_r = σ_y² / 2E", "Resilience", CYAN),
("U_t = ∫σ dε", "Toughness", GREEN),
("τ = G × γ", "Shear Stress", YELLOW),
]
y_pos = 9.5
for formula, meaning, col in formulas:
ax9.text(0.3, y_pos, formula, fontsize=8.5, color=col,
fontfamily='monospace', fontweight='bold', va='center')
ax9.text(5.2, y_pos, f"← {meaning}", fontsize=7.5, color=LGRAY, va='center')
y_pos -= 0.92
plt.savefig(OUT, dpi=150, bbox_inches='tight', facecolor=BG)
plt.close()
print(f"Saved: {OUT}")
Running Command
cd /tmp/workspace/stress-strain-pdf && python visualise_learning.py 2>&1
Running Command
ls -lh /tmp/workspace/stress-strain-pdf/visual_learning_stress_strain.png
Here's your complete visual learning package for the Stress-Strain Curve:
🎓 Visual Learning — Concept Card 1: The Journey of a Steel Rod
🎓 Visual Learning — Concept Card 2: Ductile vs Brittle vs Elastomer
🎓 Visual Learning — Concept Card 3: Properties Mind Map
📊 Full 9-Panel Visual Learning Chart
visual learning stress strain
Image · PNG
What's in the 9-panel chart:
| Panel | What you learn |
|---|---|
| 1. Full annotated curve | All 6 key points (O→F), 4 colour-coded zones, E-modulus slope shown |
| 2. Elastic region zoom | Hooke's Law slope triangle, resilience area, proportional limit |
| 3. Ductile vs Brittle vs Elastomer | 3 curves overlaid with fracture markers and callout boxes |
| 4. Toughness vs Resilience | Area-under-curve shading showing the visual difference |
| 5. Engineering vs True σ-ε | Both curves overlaid, divergence zone, conversion formulae |
| 6. 0.2% Offset method | Aluminium-style gradual yield, offset line, proof stress intersection |
| 7. Stiffness bar chart | Young's modulus of 8 materials from diamond to rubber |
| 8. Ashby-style strength map | Strength vs Toughness for metals, ceramics, polymers, composites |
| 9. Formula card | All 10 key formulae with colour coding |
This is a shared conversation. Sign in to Orris to start your own chat.