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
True stress is the stress determined by the instantaneous load acting on the instantaneous cross-sectional area True stress is related to engineering stress:
Therefore, the stress can be calculated by two formulae which are For a small elongation the engineering strain is very close to the true strain when l=1 2 lo,
Even with load-elongation data, however, it is impossible to estimate average true stress-logarithmic true strain data beyond the onset of the diffuse neck- ing