Mechanical Properties of Dental Materials

Learning goals

After reading this summary you should be able to:

• Explain why brittle restorative materials fail and why strength alone is an insufficient predictor of clinical survival.
• Define and compare core mechanical concepts (stress, strain, elastic modulus, toughness, fracture toughness, fatigue).
• Recognize common test methods and their clinical relevance (diametral tensile, flexural, biaxial flexure).
• Apply design and clinical strategies to reduce stress concentrations and fatigue failure in restorations.

Key concepts (definitions & clinical relevance)

Stress, strain and units

• Stress (σ) — force per unit area (N/m² = Pa). Typical clinical units: MPa (10⁶ Pa).
  Formula: σ = F / A.
• Strain (ε) — relative deformation (dimensionless): ε = Δl / l₀ (e.g., 0.001 = 0.1%).
• Clinical relevance: The same applied force can produce different stresses depending on contact area, shape, support, and material stiffness.

Types of stress

• Tensile stress — pulls material apart; most dangerous for brittle materials (initiates cracks).
• Compressive stress — shortens material; flaws tend to close, less likely to cause fracture.
• Shear stress — sliding force parallel to an interface; pure shear failure is uncommon in the oral environment because geometry and loading produce mixed-mode stresses.
• Flexural (bending) stress — produces a tensile surface and compressive surface separated by a neutral axis; flexural loading commonly causes tensile-driven fractures at the convex surface.

Elastic versus plastic behavior

• Elastic deformation — reversible; material returns to original shape on unloading. Quantified in the linear (Hookean) portion of the stress–strain curve.
• Plastic (permanent) deformation — irreversible; occurs once stresses exceed the proportional limit/elastic limit.
• Clinical relevance: Metals can be burnished or adjusted because they plastically deform; ceramics cannot.

Mechanical properties — definitions, units and clinical meaning

Property	Symbol/units	Definition	Clinical implication
Elastic modulus (Young’s modulus)	E (GPa or MPa)	Slope of elastic part of stress–strain curve (σ/ε) — stiffness	Higher E → less deformation under load; affects stress transfer and deformation compatibility with tooth structure
Proportional/elastic limit	— (MPa)	Max stress where stress ∝ strain	Above it, permanent deformation begins — important for adjustments/burnishing
Yield strength (proof stress)	(MPa)	Stress causing a defined small plastic strain (e.g., 0.2% offset) — metals only	Guides safe permanent deformation limits for alloys
Ultimate tensile strength (UTS)	(MPa)	Maximum engineering stress before rupture	Not reliable alone for brittle materials due to size/rate/flaw sensitivity
Toughness	(energy per volume)	Total area under stress–strain curve	Energy absorption before fracture — important for impact resistance
Fracture toughness	K_Ic (MPa·m¹/²)	Resistance to crack propagation (critical stress intensity)	Best predictor of brittle-material performance; higher K_Ic → more resistant to catastrophic crack growth
Hardness	(e.g., KHN, VHN)	Resistance to indentation/scratch	Linked to wear, abrasion of opposing enamel; influenced by strength and ductility
Fatigue / Endurance Limit	—	Stress below which infinite-cycle survival is expected	Critical because many restorations fail after many mastication cycles, not single overload
Weibull modulus	m (dimensionless)	Statistical measure of scatter in strength (higher = more reliable)	Use to estimate survival probability — important for brittle materials with non-Gaussian strength distributions

Why strength is NOT a sole reliable property for brittle dental materials

• Strength depends on specimen size, shape, loading rate, surface finish, flaw population and number of loading cycles.
• Brittle materials (ceramics, many composites, cements) fracture catastrophically at or near their elastic limit with little plastic warning.
• Fracture toughness (K_Ic) is a more fundamental, material-intrinsic descriptor of resistance to crack propagation and better predicts clinical performance for brittle materials.

Fatigue and environmental effects

• Fatigue: progressive crack growth under cyclic loading — mastication applies thousands of cycles/day.
• Static fatigue: slow crack growth under constant tensile stress (e.g., sustained wire activation or stresses in wet environments).
• Environment: aqueous oral conditions can chemically accelerate crack growth in glassy ceramics (stress corrosion).
• Clinical implication: design must minimize tensile stress amplitudes and surface flaws; clinical endurance (not single-load strength) determines long-term survival.

Tests commonly used & their interpretations

1. Diametral tensile (Brazilian) test

• Use: Estimate tensile strength of brittle disk specimens under lateral compression.
• Formula: σ_t = 2F / (π D t) (F = load; D = diameter; t = thickness).
• Note: Valid for materials with primarily elastic behavior; plasticity yields misleadingly high values.

2. Three-point and four-point flexural tests

• Three-point flexure: σ = (3 P L) / (2 w t²)
  (P = fracture load, L = support span, w = width, t = thickness)
• Four-point flexure: σ = (3 P L) / (4 w t²) — gives uniform maximum stress region, preferred if fracture location varies.
• Clinical relevance: Flexural tests simulate tensile stresses at surfaces of bridges, cantilevers and clasps better than pure compression tests.

3. Biaxial flexural (piston-on-three-ball)

• Use: Disk-shaped specimens; reduces edge-fracture artifacts. Preferred for dental ceramics.

4. Hardness tests

• Macro: Brinell, Rockwell — larger-indenter, bulk measures (metals).
• Micro: Vickers, Knoop — precise, shallow indentations for brittle materials and small regions (enamel, ceramics).
• Interpretation: Hardness relates to wear resistance and proportional limit but is not a sole predictor of fracture behavior.

5. Impact (Charpy/Izod)

• Measures: Energy required to fracture under rapid loading — relates to resilience and toughness.
• Clinical analogy: Trauma to the jaw; materials with low modulus and high strength are more impact resistant.

Design & clinical strategies to reduce fracture risk

Minimize stress concentrations

1. Surface finishing & polishing — reduce grind/processing-induced flaws.
2. Avoid sharp internal line angles — round preparation geometry.
3. Avoid notches or abrupt section changes in frameworks and clasp attachments.
4. Match elastic moduli and thermal expansion across interfaces when bonding dissimilar materials:
   • If mismatch unavoidable, design so the brittle material sustains compressive residual stress adjacent to interface.
5. Enlarge contact areas / round opposing cusps to reduce Hertzian point contact stresses.

Manage fatigue and loading

• Design to keep maximum tensile stress below endurance limit derived from cyclic testing (or conservative estimates based on Weibull/clinical data).
• Recognize bruxism/clenching as high-risk: consider tougher materials, increased dimensions, or protective appliances (nightguard).

Clinical handling considerations

• Burnishing margins (metals):
  • Works only if metal is ductile & yield strength allows plastic flow.
  • Expect elastic spring-back equal to elastic strain — only permanent (plastic) deformation reduces gaps.
  • Indication: minor marginal discrepancies on ductile alloys; contraindication: brittle alloys or ceramics.
• Adjustment of clasp arms / orthodontic wires:
  • Cold working increases hardness (strain hardening) and reduces ductility; perform adjustments in small increments.
  • Repeated bending → embrittlement and risk of fracture.

Tooth structure — mechanical contrasts & clinical implications

• Enamel
  • Higher elastic modulus, higher proportional limit, higher compressive strength.
  • Brittle; low tensile strength (~10 MPa).
  • Unsupported enamel prone to fracture.
• Dentin
  • Lower modulus (≈1/3 to 1/7 of enamel), greater toughness and plastic deformation under compression.
  • Higher tensile strength (~50 MPa) and higher resilience — better shock absorber.
• Clinical implication: restorative materials should ideally approximate the mechanical behavior of the substrate or be protected when stiffer/brittle materials are used (e.g., use supportive cores under veneering porcelain).

Statistical reliability — Weibull analysis (brief)

• Weibull distribution describes scatter in brittle-material strengths (weakest-link behavior).
• Parameters:
  • σ₀ (scale; characteristic strength ~63.2% failure)
  • m (Weibull modulus): higher m → less scatter → more reliable material.
• Use: determine stress levels corresponding to desired survival probabilities (e.g., 95% survival stress) for safe design.

Practical checklist for clinicians selecting restorative materials

1. For brittle restorations (ceramics, many composites, cements):
   • Prefer materials with higher fracture toughness (K_Ic) and a high Weibull modulus.
   • Use flexural strength and fracture toughness (not only compressive strength) in design decisions.
2. For areas subject to tensile or flexural stresses (cantilevers, thin connectors, unsupported cusps):
   • Increase cross-sectional dimensions or change geometry to reduce local tensile stress.
3. For patients with bruxism or clenching:
   • Choose tougher materials, increase dimensions, consider protective nightguards.
4. For surface contacts/occlusion:
   • Ensure contacting cusps are rounded; avoid sharp point contacts.
5. For laboratory adjustments:
   • Minimize aggressive grinding; finish and polish ceramic surfaces to reduce flaw depth.

Frequently asked clinical questions (concise answers)

Q: Why can two identical forces produce different stresses within a crown?
A: Stress = force ÷ area and depends on contact geometry, support conditions, and material stiffness. Smaller contact areas, sharper contacts, or stiffer supporting conditions produce higher localized stresses.

Q: Why do brittle restorations often fail on the convex (tensile) surface when flexed?
A: Bending induces tensile stress on the convex side; brittle materials are weakest in tension and fracture with little plastic deformation.

Q: Why is yield strength not reported for ceramics?
A: Ceramics are purely brittle — they lack a measurable plastic region; they fracture at or near the proportional (elastic) limit, so a yield point (plastic offset) cannot be defined.

Q: Why can a stiff material fail at lower apparent strength than a more flexible one?
A: A high elastic modulus (stiff) material may have low fracture toughness and fail brittlely at low strains with catastrophic crack propagation, whereas a more ductile/flexible material can plastically redistribute stress and resist crack growth.

Short reference table — formulae

Concept	Formula / note
Stress	σ = F / A
Strain	ε = Δl / l₀
Elastic modulus	E = σ / ε (linear region)
Shear modulus	G = E / [2(1 + ν)] (ν = Poisson’s ratio, typically 0.25–0.30)
Diametral tensile stress	σ_t = 2F / (π D t)
Three-point flexural stress	σ = (3 P L) / (2 w t²)
Four-point flexural stress	σ = (3 P L) / (4 w t²)
Weibull CDF	Pf = 1 - exp[-(σ/σ₀)^m]

Final clinical takeaways

• Strength alone is insufficient for designing restorations from brittle materials — prioritize fracture toughness, surface quality, geometry, and fatigue behavior.
• Minimize tensile stresses and stress concentrations (rounded geometries, polished surfaces, matched moduli at interfaces).
• Design conservatively: use Weibull-derived survival stresses or conservative lower-percentile strength data (e.g., 5–10th percentile) rather than mean strengths for prosthesis design, especially for high-risk patients (bruxers).
• Clinical adjustments (burnishing, bending) work only when the material has plasticity; ceramics and brittle composites will not plastically deform and require different corrective approaches.