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dental materials AND mechanical properties

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dental materials stress strain modulus resilience toughness ductility fracture toughness definitions

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https://pmc.ncbi.nlm.nih.gov/articles/PMC11678187/

1. Stress and strain: definitions and classification

Stress

Stress is the internal resisting force developed per unit cross-sectional area when an external force is applied.

[ \text{Stress }(\sigma)=\frac{F}{A} ]

Unit: pascal (Pa) or commonly MPa ((N/mm^2)).

Types of stress

Type	Force effect	Example in dentistry
Tensile stress	Pulls material apart	Tensile force on a bridge connector
Compressive stress	Squeezes material	Occlusal loading of restorative material
Shear stress	Causes one part to slide over another	Shearing of luting cement or composite at an interface
Torsional stress	Twisting force, producing shear	Rotation of an endodontic file
Flexural stress	Bending, with tension on one side and compression on the other	Denture base or fixed partial denture under load

Strain

Strain is the deformation produced per unit original length as a result of stress.

[ \text{Strain }(\varepsilon)=\frac{\Delta L}{L_0} ]

It is dimensionless, often expressed as a percentage.

Types of strain

Type	Description
Tensile strain	Increase in length due to tensile force
Compressive strain	Decrease in length due to compressive force
Shear strain	Angular distortion caused by shear stress
Volumetric strain	Change in volume of a material
Torsional strain	Angular deformation due to twisting

Simple figure

Tensile stress/strain        Compressive stress/strain

← F     [ specimen ]     F →       F →   [ specimen ]   ← F
         elongation                        shortening


Shear stress/strain

      → F
   ┌────────┐
   │        │
   └────────┘
      ← F
  Parallel layers slide relative to each other.

2. Stress-strain curve: drawing and interpretation

Stress
  ^
  |                         D = Ultimate tensile strength
  |                        /\
  |                       /  \
  |                      /    \ E = Fracture point
  |                     /      \
  |              C ----/        \
  |             /                 \
  |        B --/
  |       /
  |     A
  |____/________________________________> Strain
      O

Point/region	Interpretation
O-A: Proportional limit	Stress is directly proportional to strain. This is the straight-line elastic region and obeys Hooke's law.
Slope of O-A	Modulus of elasticity or Young's modulus.
A: Proportional limit	Maximum stress up to which stress is proportional to strain.
B: Elastic limit	Maximum stress a material can tolerate and still return completely to its original dimensions after unloading.
B-C: Yield region	Permanent or plastic deformation begins.
C: Yield strength	Stress at which appreciable plastic deformation occurs.
D: Ultimate tensile strength	Maximum stress sustained by the material.
D-E: Necking region	Local reduction in cross-sectional area occurs in ductile materials.
E: Fracture strength	Stress at which the specimen breaks.

Areas under the curve

Area under the elastic region: resilience.
Total area up to fracture: toughness.
A brittle material has little or no plastic region and fractures at low strain.
A ductile material shows a long plastic region before fracture.

These definitions are consistent with a dental endodontic-materials review that describes resilience as elastic energy absorption and toughness as total energy absorption before failure (NiTi biomechanics review).

3. Modulus of elasticity

Definition

Modulus of elasticity (E), or Young's modulus, is the ratio of stress to strain within the proportional elastic region.

[ E=\frac{\text{Stress}}{\text{Strain}} ]

It represents the stiffness or resistance of a material to elastic deformation.

Unit

Since strain has no unit:

[ \text{Unit of E} = \text{Pa}, \text{MPa}, \text{or GPa} ]

Measurement

It is measured using a tensile stress-strain test:

A standardized specimen is subjected to a gradually increasing tensile load.
Applied load and elongation are recorded.
Stress and strain are calculated.
The modulus of elasticity is the slope of the linear, initial part of the stress-strain curve.

[ E=\frac{\Delta \sigma}{\Delta \varepsilon} ]

Importance in dentistry

Materials with a high modulus are rigid and resist deformation, such as metals and ceramics.
Materials with a low modulus are more flexible, such as elastomeric impression materials and some resin materials.
An appropriate modulus helps distribute occlusal forces and limit deformation or fracture.
For restorations, a modulus reasonably compatible with tooth structure is desirable. Very stiff restorations may concentrate stress, whereas very flexible restorations may deform, debond, or allow marginal leakage.
In implants, a large difference in stiffness between implant and bone can contribute to stress shielding. A review of dental restorative materials notes that elastic modulus governs stiffness and deformation resistance (review of composite restorations).

4. Toughness and resilience

Toughness

Toughness is the ability of a material to absorb energy and undergo elastic plus plastic deformation before fracture.

[ \text{Toughness} = \text{total area under the stress-strain curve up to fracture} ]

A tough material resists fracture because it can absorb considerable energy.

Resilience

Resilience is the ability of a material to absorb energy during elastic deformation and release that energy on unloading without permanent deformation.

[ \text{Modulus of resilience} = \text{area under the stress-strain curve up to the elastic limit} ]

Does higher toughness always mean higher strength?

No. Toughness and strength are not the same.

Strength is the maximum stress a material can withstand.
Toughness depends on both strength and the ability to deform plastically, that is, ductility.

Examples:

A ceramic can have high compressive strength but low toughness because it fractures with little plastic deformation.
A ductile metal may be highly tough even if its strength is not the highest.

5. Fracture toughness and unit

Fracture toughness is the resistance of a material containing a crack or flaw to crack initiation and propagation under stress.

It indicates how well a material resists catastrophic fracture in the presence of a defect.

[ K_{IC} = Y \sigma \sqrt{\pi a} ]

Where:

(K_{IC}) = plane-strain fracture toughness
(Y) = geometric factor
(\sigma) = applied stress
(a) = crack length

Unit:

[ \boxed{\text{MPa}\sqrt{\text{m}}} ]

It may also be expressed as:

[ \boxed{\text{MN m}^{-3/2}} ]

Fracture toughness is particularly important for dental ceramics because microscopic flaws can propagate and cause sudden fracture.

6. Brittle materials used in dentistry and why they are called brittle

Examples

Dental porcelain and other dental ceramics
Glass ionomer cement
Zinc phosphate cement
Zinc oxide-eugenol cement
Gypsum products: impression plaster, model plaster, dental stone, die stone
Dental amalgam, relatively brittle compared with ductile metallic alloys
Acrylic resin denture base, particularly after aging or when not adequately reinforced

Why are they called brittle?

They are called brittle because they fracture with little or no plastic deformation. On a stress-strain curve, brittle materials show:

a small strain before fracture
negligible yield or plastic region
sudden failure
relatively low fracture toughness

Brittle material:                 Ductile material:

Stress                            Stress
  ^                                 ^
  |  / fracture                     |       /\
  | /                               |      /  \ fracture
  |/                                |_____/    \__
  +--------> strain                 +--------------> strain
    very small strain                 large plastic strain

7. Ductility and malleability

Ductility

Ductility is the ability of a material to undergo permanent deformation under tensile stress before fracture.

A ductile material can be drawn into wire.

Examples: gold, wrought orthodontic wire, titanium, stainless steel, cobalt-chromium alloy to a limited extent.

Malleability

Malleability is the ability of a material to undergo permanent deformation under compressive stress without fracture.

A malleable material can be hammered or rolled into thin sheets.

Example: gold is highly malleable.

Three methods for determining ductility

Percentage elongation [ %\text{ elongation} = \frac{\text{final gauge length - original gauge length}} {\text{original gauge length}} \times 100 ]
Percentage reduction in area [ %\text{ reduction in area} = \frac{\text{original cross-sectional area - final area}} {\text{original cross-sectional area}} \times 100 ]
Bend test The specimen is bent through a specified angle or around a mandrel. Greater bending without cracking or fracture indicates greater ductility.

High percentage elongation and high percentage reduction in area indicate a more ductile dental material.

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