Tensile Test Simulator
Engineering / True Stress-Strain Conversion

The fundamental conversion from engineering to true measures relies on the assumption of constant volume (no density change) and uniform deformation before necking.

Where $\sigma_{eng}= F / A_0$ (Force / Original Area) and $\varepsilon_{eng}= \Delta L / L_0$ (Length Change / Original Gauge Length). After necking begins, deformation is no longer uniform, and these formulas are not valid for the entire sample—specialized analysis of the neck region is required.

Beyond yielding, the plastic behavior of many metals is described by a power-law relationship between true stress and true plastic strain, known as the Hollomon equation.

Here, $K$ is the strength coefficient, $\varepsilon_{pl, true}$ is the true plastic strain, and $n$ is the Strain Hardening Exponent . A higher $n$ indicates greater capacity for uniform deformation, which is crucial for metal forming processes like stamping.

CAE Material Modeling: True stress-strain data from tensile tests is the direct input for finite element analysis (FEA) software like Abaqus or LS-DYNA. It defines the plastic hardening behavior in material cards (e.g., *MAT_PIECEWISE_LINEAR_PLASTICITY). Using engineering data here would lead to inaccurate predictions of crashworthiness or forming limits.

Metal Forming Process Design: In stamping car body panels, engineers use the strain hardening exponent (n-value) to predict how much the sheet metal can be stretched without tearing. A high n-value material will distribute strain more evenly, resulting in a deeper, more complex part without failure.

Predicting Necking & Failure: The condition for the onset of necking (diffuse instability) is given by $\sigma = d\sigma/d\varepsilon$. This criterion, applied to the true stress-strain curve, helps engineers determine the forming limits in processes and is the basis for constructing Forming Limit Diagrams (FLDs).

Modeling Cyclic Loading (Bauschinger Effect): When a material is loaded in tension and then compressed (like in a rolling process), the yield strength in compression is often lower. This "Bauschinger Effect," a parameter in this simulator, is modeled in CAE using kinematic hardening rules to accurately simulate cyclic plasticity and fatigue.

First, understand that yield stress is not an absolute on/off switch for a material. Even though the simulator shows the "0.2% proof stress," in actual design you apply a safety factor to set the "allowable stress," right? For example, if the yield stress of SUS304 is about 250MPa, with a safety factor of 3, the allowable stress is just over 80MPa. Confusing this and misunderstanding it as "usable up to the yield strength" increases the risk of fatigue failure or creep.

Next, it's important to recognize that the simulator's curve represents an "idealized monotonic tension" test. In practice, complex load histories (repetition, alternating compression and tension, etc.) are often applied. For instance, automotive suspension components experience not just tension but also bending and torsion simultaneously. The intuition you gain here for the "strain hardening exponent $n$" will serve as foundational knowledge when setting up material models in subsequent elastoplastic Finite Element Analysis (FEA).

Finally, remember that calculated "toughness" values depend on the specimen geometry. This simulator performs a simplified calculation of the area under the curve (the energy absorbed by the material until fracture). However, actual components often have notches, and stress concentration there can cause the same material to fracture in a brittle manner (brittle fracture). Try selecting HDPE (polyethylene) in the tool. The area under the curve is large, but under low temperatures or impact loading, it can exhibit completely different behavior. Don't take simulation results at face value; get into the habit of thinking, "this value is a guideline under ideal conditions."