18.5
True Stress and True Strain
Engineering stress is calculated as the load divided by the original, undeformed cross-sectional area. It approximates a material under load. This app…
Engineering stress is the ratio of the load and the undeformed original cross-sectional area. Engineering stress approximates strain which represents the material under load, which is relevant for ductile materials post-yield.
Engineering stress-strain diagrams are often used for convenience, but a true stress-strain diagram provides a more accurate depiction, especially with large strains.
True stress is calculated by dividing the load by the cross-sectional area of the specimen at the particular instant of deformation. As load increases, the cross-sectional area decreases, reflecting true stress.
During the necking phase, the true stress, which is proportional to the load but inversely proportional to the area, keeps increasing until the specimen ruptures.
The true strain uses successive recorded values of length. Each increment of the distance between the gauge marks, divided by the corresponding length, gives the elementary strain.
True strain is the sum of all elementary strain values, reflecting the material's behavior more accurately.
Unlike engineering stress-strain plots, true stress versus true strain diagrams remain consistent during necking and across tensile and compressive tests.
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Q1: How is true stress different from engineering stress?
Engineering stress divides load by the original undeformed cross-sectional area, while true stress divides load by the instantaneous cross-sectional area during deformation. As load increases, the cross-sectional area decreases, making true stress more accurate, especially during necking and with large strains in ductile materials.
Q2: Why does true stress continue increasing during the necking phase?
True stress remains proportional to the applied load but inversely proportional to the cross-sectional area. During necking, although load may decrease, the area decreases faster, causing true stress to keep increasing until the specimen ruptures. This behavior is accurately captured in true stress-strain diagrams.
Q3: What is true strain and how is it calculated?
True strain sums successive elementary strain increments, where each increment equals the distance change between gauge marks divided by the corresponding length. This cumulative approach reflects material behavior more accurately than engineering strain, providing consistent results across tensile and compressive tests.
Q4: When is engineering stress-strain data less accurate than true stress-strain data?
Engineering stress-strain diagrams become less accurate with large strains, particularly post-yield in ductile materials and during necking. True stress-strain diagrams maintain consistency during necking and across different test types, making them more reliable for analyzing material deformation behavior under various loading conditions.
Q5: How does cross-sectional area change affect true stress calculations?
True stress is calculated by dividing the instantaneous load by the current cross-sectional area. As deformation progresses, the area decreases, which directly increases true stress values. This inverse relationship ensures true stress accurately reflects the material's actual stress state throughout loading.
Q6: Why are true stress-strain diagrams preferred for material analysis?
True stress-strain diagrams provide accurate depiction across all deformation phases, including necking, and remain consistent for both tensile and compressive tests. Unlike engineering stress-strain diagrams used for convenience, true diagrams reflect actual material behavior, making them essential for precise engineering analysis.
Q7: What role does the gauge length play in calculating true strain?
Gauge length determines the reference points for measuring successive length changes. Each increment of distance between gauge marks, divided by the corresponding length at that instant, yields elementary strain. Accumulating these increments produces true strain, accurately capturing the material's deformation history.