Lecture 8 – Deformation and Damage Read Chapt 5 Review of terms: Normal stress, σ: Force per unit area applied perpendicular to the plane Normal strain, ε: Change in length per unit of length in the direction of the applied normal stress. Plastic strain: the strain not recovered during unloading Elastic strain: the strain recovered during unloading Degree of plasticity: (plastic strain)/(total strain) Degree of elasticity: (elastic strain)/(total strain) 2/23/2019 BAE2023 Physical Properties of Biological Materials

Lecture 8 – Deformation and Damage Review of terms: Modulus of elasticity, E: E = σ/ ε Tangent Definition: slope; Et = (σx + Δx - σ x - Δx )/ (ε x + Δx - ε x - Δx ) Poisson’s Ratio, μ: ratio of strain perpendicular to the applied force to the strain in the direction of the applied force... εz = σz/E ; εy = - μ εz ; εx = - μ εz Shear stress: F/A parallel to surface of the plane, τ Shear strain: change in angle, δ Shear Modulus, G: G = τ/δ 2/23/2019 BAE2023 Physical Properties of Biological Materials

Lecture 8 – Deformation and Damage (Notes) To determine the elastic modulus, E… for steel flat plate: for steel spherical indentor: 2/23/2019 BAE2023 Physical Properties of Biological Materials

Lecture 8 – Deformation and Damage 2/23/2019 BAE2023 Physical Properties of Biological Materials

Lecture 8 – Deformation and Damage Example of plate deformation: 2/23/2019 BAE2023 Physical Properties of Biological Materials

Lecture 8 – Deformation and Damage Example of spherical object deformation: 2/23/2019 BAE2023 Physical Properties of Biological Materials

Lecture 8 – Deformation and Damage Stacked particles (grain, seeds, dirt clods) Figure 5.1 Dropped particles Grain bin and handling damage Figure 5.3 – Table 5.13: example of product testing. Broken or damage material: determined using sieves. Bruised fruit: determined by visual inspection, spectral reflectance, Magness-Taylor pressure tester. 2/23/2019 BAE2023 Physical Properties of Biological Materials

BAE2023 Physical Properties of Biological Materials Lecture 8 HW Assignment Due 2/16 Problem 1: An apple is cut in a cylindrical shape 28.7 mm in diameter and 22.3 mm in height. Using an Instron Universal Testing Machine, the apple cylinder is compressed. The travel distance of the compression head of the Instron is 3.9 mm. The load cell records a force of 425.5 N. Calculate the stress εz , and strain σz on the apple cylinder. 2/23/2019 BAE2023 Physical Properties of Biological Materials

BAE2023 Physical Properties of Biological Materials Lecture 8 HW Assignment Due 2/16 Problem 2: A sample of freshly harvested miscanthus is shaped into a beam with a square cross section of 6.1 mm by 6.1 mm. Two supports placed 0.7 mm apart support the miscanthus sample and a load is applied halfway between the support points in order to test the Force required to fracture the sample. If ultimate tensile strength is 890 MPa, what would be the force F (newtons) required to cause this sample to fail? 2/23/2019 BAE2023 Physical Properties of Biological Materials

BAE2023 Physical Properties of Biological Materials HW Assignment Due 2/16 Problem 3: Ham is to be sliced for a deli tray. A prepared block of the ham has a bottom surface of 10 cm x 7 cm. The block is held securely in a meat slicing machine. A slicing blade moves across the top surface of the ham with a uniform lateral force of 27 N and slices a thin portion of meat from the block. The shear modulus, G, of the ham is 32.3 kPa. Estimate the deflection of the top surface with respect to the bottom surface of the block during slicing. 2/23/2019 BAE2023 Physical Properties of Biological Materials

BAE2023 Physical Properties of Biological Materials HW Assignment Due 2/16 Problem 4: Sam, the strawberry producer, has had complaints from the produce company that his strawberries are damaged during transit. Sam would like to know the force required to damage the strawberries if they are stacked three deep in their container. The damage occurs on the bottom layer at the interface with the parallel surface of the container and also at the point of contact between the layers of strawberries. An hydrostatic bulk compression test on a sample of Sam’s strawberries indicates an average bulk modulus of 225 psi. Testing of specimens from Sam’s strawberry crop shows a compression modulus E of 200 psi. The average strawberry diameter is 1.25 inches and the axial deformation due to the damage in transit averages 0.23 inches. The modulus of elasticity for Sam’s variety of strawberries is reported to be 130 psi. Estimate the force Sam’s strawberries may be encountering during transit. (Hertz method) 2/23/2019 BAE2023 Physical Properties of Biological Materials