Material Testing, the Stress-Strain Curve, and CAE
The stress-strain curve is one of the most critical inputs for finite element analysis (FEA), as it characterizes how a material deforms under load. It is typically generated from a mechanical test (most commonly tensile testing) that measures the force required to deform a specimen and the resulting change in shape. This data is essential for capturing material behavior in simulation models.
To learn more regarding material testing and characterization in support of material models for CAE, see our TestPaks or contact us to talk with our materials testing experts.
Strain Measurement
Strain is defined as the change in length divided by the original length of the specimen's gauge region. This is known as Cauchy or engineering strain and calculated as:
However, for FEA, accurate strain measurement within the gauge region is crucial. Relying on crosshead displacement introduces error due to system compliance and deformation outside the gauge section (e.g., in grips). This can distort critical properties such as modulus, yield, and failure strain.
To eliminate these artefacts, strain should be measured using extensometers, which capture deformation strictly within the gauge region. These tools ensure data reliability for use in simulation.
Because engineering strain assumes a fixed gauge length, it becomes inaccurate at higher deformations where the specimen elongates significantly. For simulations, true (or logarithmic) strain — also termed Hencky strain — which accounts for the continuous increase in gauge length, is preferred:
Stress Measurement
Stress is the applied force normalized by area. Engineering stress assumes a constant cross-sectional area (the original area):
But as materials deform — especially at higher strains — the cross-sectional area typically reduces. To account for this, true stress is used in FEA:
This formula assumes volume constancy and uniform deformation — assumptions that may break down during necking or other localized deformation. In such cases, more advanced techniques, such as Digital Image Correlation (DIC) — which enables the visualization of strain localization across the entire specimen surface — can be used to track localized strain and true cross-sectional area changes. This allows more precise determination of true strain, particularly in the plastic region, and helps identify deviations from ideal uniform deformation.
Converting Engineering to True Stress-Strain
While test labs often report engineering stress-strain, simulation software usually requires true stress-strain input. For small deformations, the difference is negligible, especially in linear materials like metals. However, for nonlinear materials (e.g., polymers, rubbers) and large strains, the error becomes significant if the conversion isn’t made.
Key Parameters from Stress-Strain Curves
Stress-strain curves contain several important points and slopes used in material modeling for FEA:
Modulus of Elasticity (Young’s Modulus)
The elastic modulus is the slope of the initial, linear portion of the stress-strain curve. However, not all materials — especially plastics — show a perfectly linear region. Consequently, different methods are used to define modulus:
- Tangent modulus: Slope at a specific point.
- Chord modulus: Slope between two defined points.
- Secant modulus: Slope from the origin to a specified strain.
In linear elastic materials (e.g., metals), these values are typically the same. In nonlinear materials, however, the choice affects simulation accuracy. For small-deformation simulations like NVH (noise, vibration, harshness), tangent or chord modulus is used. For simulations involving larger strains, secant modulus is more appropriate, as it better captures averaged stiffness.
Yield Stress
The yield stress marks the transition from elastic to plastic deformation. However, definitions vary:
- In FEA, yield is often defined as the onset of plasticity.
- In ISO 472, it is the point where strain increases without further increase in stress.
These definitions often coincide in metals but diverge in plastics, where plasticity may begin before the ISO-defined yield point. This can lead to confusion during material model development.
Failure Strain
This is the strain at which the material breaks. In ductile materials, failure is often preceded by strain localization (e.g., necking), which traditional strain measurements fail to capture. In such cases, DIC techniques are necessary for accurate measurement. Although FEA often doesn’t simulate material behavior beyond yield, failure strain becomes important in applications like crash simulation.
Complexity in Material Characterization
Because of the nuances in material behavior, interpreting stress-strain curves correctly is crucial. Many material parameters required in FEA software are idealized, but real-world data involves assumptions and approximations. Differences in how parameters like modulus and yield are computed can lead to inconsistencies between simulation and reality.
In nonlinear materials especially, curve interpretation requires careful selection of appropriate definitions and measurement methods. It’s essential that analysts understand not only the numerical values but also the methods and limitations behind their derivation.
Conclusion
The stress-strain curve is more than a graph — it's a foundational tool for building reliable FEA material models. Accurate measurements, correct strain and stress interpretations, and awareness of how key parameters like modulus and yield are defined and applied are essential for successful simulation. By understanding the underlying mechanics and limitations of stress-strain data, analysts can build better models and predict material behavior with greater fidelity.
To explore the topics discussed on this page further, see Hubert Lobo (Founder, DatapointLabs) and Brian Croop (CEO, DatapointLabs), Determination and Use of Material Properties for Finite Element Analysis (NAFEMS, 2016), Ch.3.
