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Step6: Calculate true stress and strain The stress and strain are simply calculated by giving the equations in HyperMath The equations are written inside the loop that reads the files to reduce computational effort In HyperMath language, Log is the natural logarithm Step7: Close the file The command Close(fileid) closes the file
Stress is the force per unit area upon which it acts Stress = = Force/AreaN/m2 or Pascals The symbol is called SIGMA NOTE ON UNITS The fundamental unit of stress is 1 N/m2and this is called a Pascal This is a small quantity in most fields of engineering so we use the multiples kPa, MPa and GPa
FIGURE 1 7: (a) Comparison of engineering and true stress strain curves 16 (b) Tension True curve (flow) compared to that from compression test FIGURE 1 8: Considère criterion to illustrate the onset of necking True and 19 nominal stress-strain curves are plotted along with the strain hardening rate (dashed line in the upper right corner)
Note: Hooke’s Law describes only the initial linear portion of the stress-strain curve for a bar subjected to uniaxial extension The slope of the straight-line portion of the stress-strain diagram is called the Modulus of Elasticity or Young’s Modulus E = ?/? (normal stress – strain) G = ?/? (shear stress – strain)
Figure7:Neckinganddrawingina6-packholder “True” Stress-Strain Curves Asdiscussedintheprevioussection,theengineeringstress-straincurvemustbeinterpretedwith