Lecture 2. Mechanical Behavior of Materials I PDF

IM417 – Failure Analysis Lecture 2: Mechanical Behavior of Materials I Dr. Mohamed Khamis Industrial and Management Engineering Technological Tools — Mechanical Testing — Hardness, micro-hardness, tensile, shear, physical testing — Stres...

IM417 – Failure Analysis Lecture 2: Mechanical Behavior of Materials I Dr. Mohamed Khamis Industrial and Management Engineering Technological Tools — Mechanical Testing — Hardness, micro-hardness, tensile, shear, physical testing — Stress Analysis / FEA — Magnitude, principal direction, sensitivity — Instrumentation — Strain Gages, accelerometers, thermocouples, ect. — Non-Destructive Testing (NDT) 2/29 Mechanical Testing — Up to 100,000 lbf in the lab — Over 1 million lbf in the field Output Tensile strength, Necking Hooke’s law — Stress versus Strain Poisson’s ratio — Elastic Deformation Modulus of resilience (Er) — Plastic Deformation Tensile toughness — Elastic limit Ductility 3/29 Measuring Components 4/29 5 Stress Vs Strain Mechanical Properties — Properties that deal with elastic or inelastic behavior of a material under load. — Deal directly with behavior of materials under applied forces. — Properties are described by applied stress and resulting strain, or applied strain and resulting stress. Example: 100 kg force applies to end of a rod results in a stress applied to the end of the rod causing it to stretch or elongate, which is measured as strain. 6/29 Stress Vs Strain Mechanical Properties — Strength: ability of material to resist application of load without rupture. – Ultimate strength- maximum force per cross section area. – Yield strength- force at yield point per cross section area. — Stiffness: resistance of material to deform under load while in elastic state. – Stiffness is usually measured by the Modulus of Elasticity (Stress/strain) – Steel is stiff (tough to bend). Some beds are stiff, some are soft (compliant) 7/29 Testing Procedures Mechanical Testing — Primary measurements involved are load applied and effects of load application. — Parameters of test: method of loading, condition of the specimen during the test and surrounding conditions (environment) during testing. Primary types of tests Tensile, Compression, Shear, Torsion, Flexure 8/29 Mechanical Test Considerations Tests classification- load application — Kind of stress induced: single load or multiple loads — Rate at which stress is developed: static versus dynamic — Number of cycles of load application: single versus fatigue 9/29 Tensile Test — Unidirectional force is applied to a specimen in the tensile test by means of the movable crosshead. — The cross-head movement can be performed using screws or a hydraulic mechanism. 10/29 Tensile Stress-Strain Curves for Different Materials 11/29 Stiffness and Resilience Stiffness is the extent to which an object resists deformation in response to an applied force. The complementary concept is flexibility or pliability: the more flexible an object is, the less stiff it is. The stiffness, k, of a body is a measure of the resistance offered by an elastic body to deformation (for example, stretching or compression of a rod), the stiffness is defined as: k=F/d Where F, is the force on the body d is the displacement (i.e. change length) 12/29 Stiffness and Resilience Resilience is the ability of a material to absorb energy when it is deformed elastically, and release that energy upon unloading. The modulus of resilience is defined as the maximum energy that can be absorbed per unit volume without creating a permanent distortion. It can be calculated by integrating the stress– strain curve from zero to the elastic limit. Ur, is the modulus of resilience, σy is the yield strength, εy is the yield strain, and E is the Young's modulus. 13/29 The Output of Tensile Test , 0.505-in diameter 14/29 Yield Strength Figure (a) Determining the 0.2% offset yield strength in gray cast ion, and (b) upper and lower yield point behavior in a low-carbon steel 15/29  Yield Strength & Plasticity Offset Yield Strength The most common offset is 0.2%. Method to determine the yield strength of materials that do not have an easily discernible yield point. 16/29 Perfectly Plastic 17/29 Strain-Hardening 18/29 Engineering & True Stresses-Strain Engineering stress: 19/29 Engineering & True Stresses-Strain 20/29 Engineering & True Strains Engineering axial strain 21/29 Example: Young’s Modulus of Aluminum Alloy From the data in Example, calculate the modulus of elasticity of the aluminum alloy. Use the modulus to determine the length after deformation of a bar of initial length of 50 in. Assume that a level of stress of 30,000 psi is applied. Solution 22/29 Example: True Stress, True Strain Calculations Compare engineering stress and strain with true stress and strain for the aluminum alloy in slide 12, at (a) the maximum load and (b) fracture. The diameter at maximum load is 0.497 in. and at fracture is 0.398 in. Solution 23/29 Solution (Continued) 24/29 Mechanical Test Modes Primary types of loading tension shear compression flexure torsion 25/29 Compression Test Specimens are short and large in diameter. Stress is Force per unit area. Strain is the ratio of the change in length and the original length. (Deformation). s s= F lf lo Stress, A e Strain, 26/29 Shear Test Principles — Direct shear occurs when parallel forces are applied in the opposite Stress,t direction. τ = F/A — Single shear occurs on a single plane. — Double shear occurs on two planes simultaneously. Strain, g Single shear Double shear 27/29 Torsion Test Principles — Torsional shear stress or Torsional stress is the shear stress produced in the shaft due to the twisting. This twisting in the shaft is caused by the couple acting on it. – Torsional forces developed in a material are the result of an applied torque. – Torque is Force x distance. – t= Torsional stress, r= radius, J= second moment of inertia. 28/29 Thanks