CHE 333 Class 11 Mechanical Behavior of Materials
Elastic Deformation. Consider a metal rod fixed at one end. At the other end a load can be applied by some manner. When a small amount of load is applied, if the length of the metal rod was measured it would be longer. If the load is removed, and the rod measured again, it would return to the original length. It is said that the deformation was recovered. This type of deformation is ELASTIC, that is all recovered on load removal. It was also found that the extension of the rod was directly proportional to the load applied. Load extension data would be as shown in the diagram. Service loads should be ELASTIC Load Extension
Plastic Deformation Load Following elastic deformation, the load extension curve is no longer linear, as shown in the diagram. After the linear elastic portion, a non linear region starts which indicates the start of PLASTIC deformation. If the load is removed at a point after plastic deformation is initiated the metal rod will not return to the same length as the initial length. It will be longer by the amount of plastic deformation. The new increase length is the plastic deformation. In this case all the deformation was not recovered. The elastic portion is recovered but not the plastic deformation. The load removal curve decreases parallel to the elastic deformation line. Load Removal Final length after load removal Extension
Stress Strain Curves Stress The load extension data can be transformed into Stress Strain data by normalising with respect to material dimensions. The stress is the load divided by the original cross sectional area. s = L/A s – stress , units MPa, or psi or ksi L – load applied A – original cross sectional area The strain is the increase in length normalised by the original length. e = Dl/l e – strain – dimensionless (in/in) Dl – increase in length l – original length Strain is often given in percent so x100 As the normalisations are by constants the shapes of the curves stays the same. Strain rate is e/t. Most materials are strain rate sensitive that is their mechanical behavior depends on the rate of deformation. Strain
Hooke’s Law and Young’s Modulus Stress Hooke’s Law is concerned with Elasticity. s = Ee Stress is proportional to strain, But only in the elastic region. This is the “elasticity” or elastic Modulus of materials, sometimes Called “Young’s Modulus”. Metal Youngs Mod 106psi Aluminum 11 Gold 16 Copper 28 Iron (BCC) 41 Yield Stress Strain
Yield Stress Ultimate Tensile Stress The Yield Stress is at the onset of plastic deformation. The Ultimate Tensile Stress is the maximum stress during the stress strain test. Manufacturing between YS and UTS The strain to failure can be measured from the stress strain data, The 0.2% yield stress is used for materials such as steel as the yield point is sometimes difficult to determine. At 0.2% strain a line is drawn parallel to the elastic portion of the data until it intersects the plastic portion of the data. The stress level at this point is the 0.2% yield stress. (0.002 strain) Stress Ultimate Tensile Stress 0.2% YS Yield Stress Strain at Failure Strain
Brittle Behavior Stress Failure at this stress Brittle materials exhibit little on no plastic deformation region. Only elastic deformation is found. The energy of failure is then the area under the stress stain curve, which for a brittle material is the area of a right angel triangle, or half base multiplied by the height. Or half the strain at failure multiplied by the stress at failure. Plastic deformation adds a considerable amount of energy to the failure process. Ceramics and martensitic steels show this behavior. Energy of failure is the area under the stress strain curve. For brittle materials it is half the strain multiplied by the failure stress. Strain
Reduction of Area At the UTS, for metals local deformation starts, and thereafter the deformation is concentrated locally. This causes a “NECK” to occur shown above along with the crack at failure.The cross section is reduced at the failure point compared to the region outside the neck. One measure of “DUCTILITY” besides elongation at failure is “reduction of area” ROA = final cross sectional area/ original cross sectional area
Cup and Cone Failure Final failure in round bar is often characterized for a ductile material as a “Cup and Cone” failure. An example is shown. The fracture starts in the interior of the material and spreads internally until only a small annulus of material remains. This then shears at 45o to the applied stress. The more ductile the material the larger the shear lip.
Sheet Tensile Sample A sheet material tensile sample is shown above. ASTM has standard dimensions. At either end is a grip area, and in the center is the gauge length which is a narrower section to ensure failure outside the grip area effects. The thickness and width of the sample need to be known to calculate the stress data and the original length to calculate the strain at failure.
Failed Sample Metal A failed sample is compared to a new untested sample. Note the failure is at 45o to the applied stress. The local deformation in this case is very near the failure point. ROA Data would be very difficult in this case. Elongation at failure would be more useful
Failed Sample - Polymer A failed polymer sample has a large elongation at failure in comparison to the metal sample. Sample is 0.5 in wide to provide a scale.
Polymer Stress Strain Curve Stress Strain Polymers generally have low elastic modulus and long elongations to failure compared to Metals.
Homework • Draw a stress strain curve for a ductile material indicating yield stress, UTS, strain to failure. • Draw the stress strain curve for a brittle material. • Briefly describe strain rate sensitivity.