The capacity of material to absorb and release strain energy within elastic limit is known as. What will be the strain energy stored in the metallic bar of cross sectional area of 2 cm2 and gauge length of 10 cm if it stretches 0. Suggested Test Series. Suggested Exams.
More Strength of Materials Questions Q1. A box of weight kN shown in the figure is to be lifted without swinging. For a beam having cross-section as T, which is a correct statement?
Elastic-Plastic B. Rigid Plastic C. Elastic-perfectly Plastic D. Perfectly Plastic. A cantilever of length 1. The bending moment at the center of the beam is 2 kNm. The reactions at the ends are:. A material yields under the following state of plane stress shown in the figure, as per Von Mises criterion, the yield stress of the material is:.
Which quantity will not be zero for a plane strain problem in an x-y plane? Testbook Edu Solutions Pvt. Thus, every time we use the word strain, it will refer to normal strain.
Once we understand normal strain, it is easy to extend the same understanding to the other two. When you try to squeeze it, it offers resistance. The resistance offered is the induced stress while the change in dimension represents the strain. Strain causes stress. When applying force that leads to deformation, a material tries to retain its body structure by setting up internal stresses. The most common method for plotting a stress and strain curve is to subject a rod of the test piece to a tensile test.
This is done using a Universal Testing Machine. It has two claws which hold the two extremes of the rod and pull it at a uniform rate. The force applied and the strain produced is recorded until a fracture occurs.
The two parameters are then plotted on an X-Y graph to get the familiar graph. The stress-strain curve is a graph that shows the change in stress as strain increases.
It is a widely used reference graph for metals in material science and manufacturing. There are various sections on the stress and strain curve that describe different behaviour of a ductile material depending on the amount of stress induced.
Stress and strain curves for brittle, hard but not ductile and plastic materials are different. The curve for these materials is simpler and can be learned very easily. We shall focus on the stress-strain curve of ductile materials. This principle of physics talks about elasticity and how the force required to extend or compress an elastic object by a certain distance is proportional to that distance.
More force produces more distance. That means stress is directly proportional to strain. This is because metals exhibit elasticity up to a certain limit. Almost all metals behave like an elastic object over a specific range. This range varies for different metals and is affected by factors such as mechanical properties , atmospheric exposure corrosion , grain size, heat treatment , and working temperature.
When the testing machine starts pulling on the test piece, it undergoes tensile stress. The strain will be proportional to stress. It means that the ratio of stress to strain will is a constant.
There is no permanent deformation either. The metal will behave like a spring and return to its original dimension on the removal of load. The point up to which this proportional behaviour is observed is known as the proportional limit.
With increasing stress, strain increases linearly. In the diagram above, this rule applies up until the yields strength indicator. It is defined as the ratio of longitudinal stress to strain within the proportional limit of a material. Also known as modulus of resilience, it is analogous to the stiffness of a spring.
As the test piece is subjected to increasing amounts of tensile force, stresses increase beyond the proportional limit.
The strain increases at a faster rate than stress which manifests itself as a mild flattening of the curve in the stress and strain graph. This is the part of the graph where the first curve starts but has not yet taken a turn downwards. The change in dimension within the elastic limit is thus temporary and reversible.
The elastic limit of a material ascertains its stability under stress. If the load is greater than the yield strength, the result will be unwanted plastic deformation. When the test piece is pulled further on the testing machine, the property of elasticity is lost. This aligns with the start of the strain hardening region in the stress-strain graph. The yield strength point is where the plastic deformation of the material is first observed.
If the material is unclamped from the testing machine beyond this point, it will not return to its original length. The material constantly rearranges itself and tends to harden.
The plastic deformation continues to occur with increasing stress. In due time, a narrowing of cross-section will be observed at a point on the rod. This phenomenon is known as necking. The stress is so high that it leads to the formation of a neck at the weakest point of the rod. You can see this happen in the video above. The stress-strain curve also shown the region where necking occurs. Its starting-point also gives us the ultimate tensile strength of a material.
Ultimate tensile strength shows the maximum amount of stress a material can handle. Reaching this value pushes the material towards failure and breaking.
Once in the necking region, we can see that the load does not have to increase for further plastic deformation. A fracture will occur at the neck usually with a cup and cone shape formation at either end of the rod.
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