Lecture 8 Announcements NOTHING DUE TODAY!!!!!  HW#5 due MONDAY, 2/5 HW#6 due Wednesday, 2/7 HW#7 due MONDAY, 2/12 (you have 3 extra days) 1/26/07 BAE2022/BAE4400 Physical Properties of Biological Materials

Deformation and Viscoelasticity Chapter 4, pg. 111 - 169 Shearing Stresses Shear stress: force per unit area acting in the direction parallel to the surface of the plane,τ Shear strain: change in the angle formed between two planes that are orthogonal prior to deformation that results from application of sheer stress, γ 1/26/07 BAE2022/BAE4400 Physical Properties of Biological Materials

Deformation and Viscoelasticity Chapter 4, pg. 111 - 169 Shear modulus: ratio of shear stress to shear strain, G = τ/γ Measured with parallel plate shear test 1/26/07 BAE2022/BAE4400 Physical Properties of Biological Materials

Deformation and Viscoelasticity Chapter 4, pg. 111 - 169 1/26/07 BAE2022/BAE4400 Physical Properties of Biological Materials

Deformation and Viscoelasticity Chapter 4, pg. 111 - 169 Problem example 1/26/07 BAE2022/BAE4400 Physical Properties of Biological Materials

Deformation and Viscoelasticity Chapter 4, pg. 111 - 169 Dilitational stress or strain causes a change in volume (usually normal stress or strain) Deviatoric stress or strain causes a change in shape (usually shear stress or strain) Bulk modulus K=avg. normal stress/dilatation Dilatation = (Vf-V0)/V0 Average stress: uniform hydrostatic gauge pressure ΔP SO…. K= ΔP / (ΔV/V0) 1/26/07 BAE2022/BAE4400 Physical Properties of Biological Materials

Deformation and Viscoelasticity Chapter 4, pg. 111 - 169 Apples compress easier than potatoes so they have a smaller bulk modulus, K -78 MPa vs. -3.6 MPa K-1 =bulk compressibility Strain energy density: area under the loading curve of stress-strain diagram Sharp drop in curve = failure 1/26/07 BAE2022/BAE4400 Physical Properties of Biological Materials

Deformation and Viscoelasticity Chapter 4, pg. 111 - 169 Area under curve until it fails = toughness Failure point = bioyield point Resilience: area under the unloading curve Resilient materials “spring back”…all energy is recovered upon unloading Hysteresis = strain density - resilience 1/26/07 BAE2022/BAE4400 Physical Properties of Biological Materials

Deformation and Viscoelasticity Chapter 4, pg. 111 - 169 Tensile testing Not as common as compression testing Harder to do See figure 4.12 page 132 1/26/07 BAE2022/BAE4400 Physical Properties of Biological Materials

Deformation and Viscoelasticity Chapter 4, pg. 111 - 169 Tensile testing 1/26/07 BAE2022/BAE4400 Physical Properties of Biological Materials

Deformation and Viscoelasticity Chapter 4, pg. 111 - 169 Stress Relaxation: Figure 4.10 pg 129 Material is deformed to a fixed strain and strain is held constant…stress required to hold strain constant decreases with time. Creep: Figure 4.11 pg. 130 A continual increase in deformation (strain) with time with constant load 1/26/07 BAE2022/BAE4400 Physical Properties of Biological Materials

Deformation and Viscoelasticity Chapter 4, pg. 111 - 169 Bending: E=modulus of elasticity D=deflection, F=force, I = moment of inertia E=L3(48DI)-1 I=bh3/12 1/26/07 BAE2022/BAE4400 Physical Properties of Biological Materials

Deformation and Viscoelasticity Chapter 4, pg. 111 - 169 Can be used for testing critical tensile stress at failure Max tensile stress occurs at bottom surface of beam σmax=3FL/(2bh2) 1/26/07 BAE2022/BAE4400 Physical Properties of Biological Materials

Deformation and Viscoelasticity Chapter 4, pg. 111 - 169 Contact Stresses (handout from Mohsenin book) Hertz Problem of Contact Stresses 1/26/07 BAE2022/BAE4400 Physical Properties of Biological Materials

BAE2022/BAE4400 Physical Properties of Biological Materials HW#7 Assignment Problem 1: One half of a mung bean seed is shaped into a beam with a square cross section of 1.2 mm by 1.2 mm. The sample beam is supported at two points 0.4 mm apart and a load is applied halfway between the support points. If the ultimate tensile strength is 6.75 MPa, what would be the force F (newtons) required to cause the sample to fail? 1/26/07 BAE2022/BAE4400 Physical Properties of Biological Materials

BAE2022/BAE4400 Physical Properties of Biological Materials HW#7 Assignment Problem 2: A block of salami has a bottom surface of 5 cm x 8 cm. The block is held securely in a meat slicing machine. The blade that moves across the top surface of the salami applies a uniform lateral force of 18 N. The shear modulus, G, of the salami is 2.2 kPa. Estimate the how far the top surface of the salami will move compared to the bottom surface. 1/26/07 BAE2022/BAE4400 Physical Properties of Biological Materials