Stress Strain Curve
Content
STRESS-STRAIN DIAGRAM FOR MILD STEEL
The stress-strain diagram for a ductile material like mildsteel is shown in Fig. 1.13. The curve starts from the origin , showing thereby that there is no initial stress of strain in the specimen. Upto point A, Hooke s law is obeyed and stress is proportional to strain. Therefore, OA is a straight line. Point A is called the limit of proportionality. Upto point B, the material remains elastic, i.e. on removal of the load, no permanent set is formed. AB is not a straight line. Point B is called the elastic limit point. Beyond point B, the material goes to the plastic stage until the upper yield point C is reached. At this point the crosssectional area of the material starts decreasing and the stress decreases to a lower value to point D, called the lower yield point. Between DE, the specimen elongates by a considerable amount without any increase in stress. From point E onwards, the strain hardening phenomena becomes predominant and the strength of the material increases thereby requiring more stress for deformation, unitl point F is reached. Point F is called the ultimate point and the corresponding stress is called the ultimate strength. At point F, necking of the material begins and the cross-sectional area decreases at a rapid rate. The apparent stress deceases but the actual or true stress goes on increasing until the specimen breaks at point C, called the point of fracture. The fracture of ductile material is of the cup and cone type. The phenomena of yielding and necking is not exhibited by brittle materials. The Ultimate strength is calculated at 0.2 per cent of maximum strain.
The shape and magnitude of the stress-strain curve of a metal will depend on its composition, heat treatment, prior history of plastic deformation, and the strain rate, temperature, and state of stress imposed during the testing. The parameters, which are used to describe the stress-strain curve of a metal, are the tensile strength, yield strength or yield point, percent elongation, and reduction of area. The first two are strength parameters; the last two indicate ductility. An example of the engineering stress-strain curve for a typical engineering alloy is shown in Figure 1. From it some very important properties can be determined. The elastic modulus, the yield strength, the ultimate tensile strength, and the fracture strain are all clearly exhibited in an accurately constructed stress strain curve.
Figure 1: An example of the engineering stress strain curve for a typical engineering alloy The elastic modulus, E (Young’s modulus) is the slope of the elastic portion of the curve (the steep, linear region) because E is the proportionality constant relating stress and strain during elastic deformation: σ = Eε. The 0.2% offset yield strength is the stress value, σ0.2%YS of the intersection of a line (called the offset) constructed parallel to the elastic portion of the curve but offset to the right by a strain of 0.002. It represents the onset of plastic deformation.
The ultimate tensile strength is the engineering stress value or σuts, at the maximum of the engineering stress-strain curve. It represents the maximum load, for that original area, that the sample can sustain without undergoing the instability of necking, which will lead inexorably to fracture. The fracture strain is the engineering strain value at which fracture occurred. At the outset, though, a clear distinction must be made between a true stress-true strain curve and an engineering stress-engineering strain curve. The difference is shown in Figure 2, which are plotted, on the same axes, the stress-strain curve and engineering stress-strain curve for the same material. The difference is also evident in the definitions of true stress-true strain and engineering stress-engineering strain.
Figure 2: Comparison of engineering and true stress-strain curves The engineering stress is the load borne by the sample divided by a constant, the original area. The true stress is the load borne by the sample divided by a variable the instantaneous area. Note that the true stress always rises in the plastic, whereas the engineering stress rises and then falls after going through a maximum. The maximum represents a significant difference between the engineering stress-strain curve and the true stress-strain curve. In the engineering stress-strain curve, this point
indicates the beginning of necking. The ultimate tensile strength is the maximum load measured in the tension test divided by the original area. The difference between True Stress and Engineering Stress Think about pulling a bar in tension. Load divided by cross-sectional area is force, or stress. But what cross section are you considering? Before starting pull, the bar had a known cross-section of (lets say) 0.5" wide x metal thickness. It's easy to measure these, since it is your starting material. At any load, the engineering stress is the load divided by this initial cross- area. While you are pulling, the length increases, but the width and thickness shrink. At any load, the true stress is the load divided by the cross-area at that instant. Unless thickness and width are being monitored continuously during the test, you cannot calculate true stress. It is, however, a much better representation of how the material behaves as it is being deformed, which explains its use in forming simulations. In circle grid analysis, engineering strain is the % expansion of the circle compared to the initial diameter of the circle. The relationships between engineering values and true values are: σ = s (1+e) ε = ln (1+e) Where "s" and "e" are the engineering stress and strain, respectively, and " " and " " are the true stress and strain, respectively.
The stress-strain diagram for a ductile material like mildsteel is shown in Fig. 1.13. The curve starts from the origin , showing thereby that there is no initial stress of strain in the specimen. Upto point A, Hooke s law is obeyed and stress is proportional to strain. Therefore, OA is a straight line. Point A is called the limit of proportionality. Upto point B, the material remains elastic, i.e. on removal of the load, no permanent set is formed. AB is not a straight line. Point B is called the elastic limit point. Beyond point B, the material goes to the plastic stage until the upper yield point C is reached. At this point the crosssectional area of the material starts decreasing and the stress decreases to a lower value to point D, called the lower yield point. Between DE, the specimen elongates by a considerable amount without any increase in stress. From point E onwards, the strain hardening phenomena becomes predominant and the strength of the material increases thereby requiring more stress for deformation, unitl point F is reached. Point F is called the ultimate point and the corresponding stress is called the ultimate strength. At point F, necking of the material begins and the cross-sectional area decreases at a rapid rate. The apparent stress deceases but the actual or true stress goes on increasing until the specimen breaks at point C, called the point of fracture. The fracture of ductile material is of the cup and cone type. The phenomena of yielding and necking is not exhibited by brittle materials. The Ultimate strength is calculated at 0.2 per cent of maximum strain.
The shape and magnitude of the stress-strain curve of a metal will depend on its composition, heat treatment, prior history of plastic deformation, and the strain rate, temperature, and state of stress imposed during the testing. The parameters, which are used to describe the stress-strain curve of a metal, are the tensile strength, yield strength or yield point, percent elongation, and reduction of area. The first two are strength parameters; the last two indicate ductility. An example of the engineering stress-strain curve for a typical engineering alloy is shown in Figure 1. From it some very important properties can be determined. The elastic modulus, the yield strength, the ultimate tensile strength, and the fracture strain are all clearly exhibited in an accurately constructed stress strain curve.
Figure 1: An example of the engineering stress strain curve for a typical engineering alloy The elastic modulus, E (Young’s modulus) is the slope of the elastic portion of the curve (the steep, linear region) because E is the proportionality constant relating stress and strain during elastic deformation: σ = Eε. The 0.2% offset yield strength is the stress value, σ0.2%YS of the intersection of a line (called the offset) constructed parallel to the elastic portion of the curve but offset to the right by a strain of 0.002. It represents the onset of plastic deformation.
The ultimate tensile strength is the engineering stress value or σuts, at the maximum of the engineering stress-strain curve. It represents the maximum load, for that original area, that the sample can sustain without undergoing the instability of necking, which will lead inexorably to fracture. The fracture strain is the engineering strain value at which fracture occurred. At the outset, though, a clear distinction must be made between a true stress-true strain curve and an engineering stress-engineering strain curve. The difference is shown in Figure 2, which are plotted, on the same axes, the stress-strain curve and engineering stress-strain curve for the same material. The difference is also evident in the definitions of true stress-true strain and engineering stress-engineering strain.
Figure 2: Comparison of engineering and true stress-strain curves The engineering stress is the load borne by the sample divided by a constant, the original area. The true stress is the load borne by the sample divided by a variable the instantaneous area. Note that the true stress always rises in the plastic, whereas the engineering stress rises and then falls after going through a maximum. The maximum represents a significant difference between the engineering stress-strain curve and the true stress-strain curve. In the engineering stress-strain curve, this point
indicates the beginning of necking. The ultimate tensile strength is the maximum load measured in the tension test divided by the original area. The difference between True Stress and Engineering Stress Think about pulling a bar in tension. Load divided by cross-sectional area is force, or stress. But what cross section are you considering? Before starting pull, the bar had a known cross-section of (lets say) 0.5" wide x metal thickness. It's easy to measure these, since it is your starting material. At any load, the engineering stress is the load divided by this initial cross- area. While you are pulling, the length increases, but the width and thickness shrink. At any load, the true stress is the load divided by the cross-area at that instant. Unless thickness and width are being monitored continuously during the test, you cannot calculate true stress. It is, however, a much better representation of how the material behaves as it is being deformed, which explains its use in forming simulations. In circle grid analysis, engineering strain is the % expansion of the circle compared to the initial diameter of the circle. The relationships between engineering values and true values are: σ = s (1+e) ε = ln (1+e) Where "s" and "e" are the engineering stress and strain, respectively, and " " and " " are the true stress and strain, respectively.
