Lecture 26: Mechanical Properties I: Metals & Ceramics Reading assignment: Callister 6.1-6.3, 6.5-6.9, 13.8-13.9 Learning objectives: Understand the difference between elastic and plastic deformation Know how to determine mechanical properties from the results of a tensile test Elastic modulus • Yield strength Tensile strength • Strain to failure Understand how the mechanical properties of ceramics differ from those of ductile metals Lecture 26, summer 2007 Mechanical Properties I: Metals & Ceramics ENGR 145, Chemistry of Materials Case Western Reserve University

Engineering Stress & Strain [Callister 6.2] tension compression from Callister Lecture 26, summer 2007 Mechanical Properties I: Metals & Ceramics ENGR 145, Chemistry of Materials Case Western Reserve University

Elasticity vs. Plasticity [Callister 6.2] Elastic behavior 0 when 0 Reversible deformation — no permanent shape change after load is removed Plastic behavior ≠0 when 0 Some strain remains after load has been removed Lecture 26, summer 2007 Mechanical Properties I: Metals & Ceramics ENGR 145, Chemistry of Materials Case Western Reserve University

Poisson’s Ratio [Callister 6.5] Elastic dimensional change will occur transverse to applied uniaxial load: Poisson’s ratio Lecture 26, summer 2007 Mechanical Properties I: Metals & Ceramics ENGR 145, Chemistry of Materials Case Western Reserve University

Elastic Behavior [Callister 6.3] Stress-strain curve for loading … … is retraced on unloading Linear elastic behavior: Hooke’s law modulus of elasticity (a.k.a. Young’s modulus) Note: not all elastic behavior is linear (see e.g. Callister Figure 6.6) … … but all elastic behavior is reversible Lecture 26, summer 2007 Mechanical Properties I: Metals & Ceramics ENGR 145, Chemistry of Materials Case Western Reserve University Callister Fig. 6.5

Modulus of Elasticity and the Interatomic Potential [Callister 6.3] Recall that energy between atoms depends on their separation Recall also that Minimum in energy  zero net force Applying tension or compression raises energy of material compression tension Callister Fig. 2.8b Lecture 26, summer 2007 Mechanical Properties I: Metals & Ceramics ENGR 145, Chemistry of Materials Case Western Reserve University

Modulus of Elasticity and the Interatomic Potential [Callister 6.3] F = d(energy)/dr Modulus of elasticity  dF/dr E  d2(energy)/dr2 — curvature of interatomic potential near ro Lecture 26, summer 2007 Mechanical Properties I: Metals & Ceramics ENGR 145, Chemistry of Materials Case Western Reserve University Callister Fig. 2.8 a

Modulus of Elasticity and the Interatomic Potential [Callister 6.3] Modulus of elasticity  dF/dr high modulus low modulus Lecture 26, summer 2007 Mechanical Properties I: Metals & Ceramics ENGR 145, Chemistry of Materials Case Western Reserve University Callister Fig. 6.7

Mechanical Properties of Metals — Elastic Behavior High modulus  strong bonding (high curvature of interatomic potential near ro) (from Callister) Lecture 26, summer 2007 Mechanical Properties I: Metals & Ceramics ENGR 145, Chemistry of Materials Case Western Reserve University

Elastic Modulus: Temperature Dependence [Callister 6.3] E  gradually as T  Callister Fig. 2.8 Callister Fig 6.8 Lecture 26, summer 2007 Mechanical Properties I: Metals & Ceramics ENGR 145, Chemistry of Materials Case Western Reserve University

Mechanical Properties of Metals [Callister 6.5] Plastic behavior: some strain remains after removal of load Yield strength: stress that will result in a specified residual strain 0.2% yield strength 0.002=0.2%) Lecture 26, summer 2007 Mechanical Properties I: Metals & Ceramics ENGR 145, Chemistry of Materials Case Western Reserve University

Mechanical Properties of Metals [Callister 6.5] Plastic behavior in a tensile test Yielding Tensile strength (M) (a.k.a. ultimate tensile strength) Necking Fracture (F) Callister Fig. 6.11 Lecture 26, summer 2007 Mechanical Properties I: Metals & Ceramics ENGR 145, Chemistry of Materials Case Western Reserve University

Mechanical Properties of Metals [Callister 6.5] Brittle vs. ductile Two measures of ductility: % elongation % area reduction Callister Fig. 6.13 Lecture 26, summer 2007 Mechanical Properties I: Metals & Ceramics ENGR 145, Chemistry of Materials Case Western Reserve University

Mechanical Properties of Metals — Plastic Behavior Lecture 26, summer 2007 Mechanical Properties I: Metals & Ceramics ENGR 145, Chemistry of Materials Case Western Reserve University

Plastic Behavior: Effects of Temperature Callister Fig. 6.14 Lecture 26, summer 2007 Mechanical Properties I: Metals & Ceramics ENGR 145, Chemistry of Materials Case Western Reserve University

Modulus of Resilience [Callister 6.6] Measure of a material’s capacity to absorb mechanical energy elastically Area under stress-strain curve has units of energy per unit volume Approximate this integral with: Callister Fig. 6.15 Lecture 26, summer 2007 Mechanical Properties I: Metals & Ceramics ENGR 145, Chemistry of Materials Case Western Reserve University

Modulus of Toughness [Callister 6.6] A measure of energy absorbed during fracture Area under stress-strain curve has units of energy per unit volume Approximate this area as or Lecture 26, summer 2007 Mechanical Properties I: Metals & Ceramics ENGR 145, Chemistry of Materials Case Western Reserve University Callister Fig. 6.13

True Stress and Strain [Callister 6.7] Engineering stress and strain: based on initial dimensions True stress and strain: based on instantaneous dimensions (i) Callister Fig. 6.1 Lecture 26, summer 2007 Mechanical Properties I: Metals & Ceramics ENGR 145, Chemistry of Materials Case Western Reserve University

True Stress and Strain [Callister 6.7] Engineering stress and strain: based on initial dimensions True stress and true strain: based on instantaneous dimensions Callister Fig. 6.16 Start of necking Lecture 26, summer 2007 Mechanical Properties I: Metals & Ceramics ENGR 145, Chemistry of Materials Case Western Reserve University

Mechanical Properties of Ceramics [Callister 13.8] Virtually no plasticity at room T Strain to failure typically < 0.2% Linear to fracture Lecture 26, summer 2007 Mechanical Properties I: Metals & Ceramics ENGR 145, Chemistry of Materials Case Western Reserve University Callister Fig. 13.29

Mechanical Properties of Ceramics [Callister 13.8] Flexural strength: measured in 3-point bending a.k.a. modulus of rupture, 3-point bend strength, fracture strength Compression Tension rectangular cross-section circular cross-section Lecture 26, summer 2007 Mechanical Properties I: Metals & Ceramics ENGR 145, Chemistry of Materials Case Western Reserve University Callister Fig. 13.28

Mechanical Properties of Ceramics [Callister 13.8] Moduli usu. higher than for metals • Wide spread in strengths Lecture 26, summer 2007 Mechanical Properties I: Metals & Ceramics ENGR 145, Chemistry of Materials Case Western Reserve University