Testing for Rate-Dependent Material Models for CAE
Rate dependency, or strain rate sensitivity, describes how a material's mechanical properties, such as strength, stiffness, and ductility, can change depending on how quickly it's deformed or loaded. This phenomenon is crucial in various applications ranging from automotive crashworthiness, where materials must withstand high-speed impacts, to high-speed manufacturing processes.
For instance, materials may exhibit increased strength at higher strain rates, as is often seen in metals, while viscoelastic materials like polymers can show significantly different responses, acting more stiffly at faster deformation rates and less so at slower rates. Understanding and modeling rate-dependent behavior is therefore essential for predicting material performance under various dynamic loading conditions and for designing components that can function reliably in such environments.
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.
Importance of Capturing Rate Dependency
In drop, impact or crash simulations, materials are subjected to a wide range of strain rates, which significantly affect mechanical response. It's critical to understand that strain rate is different from impact velocity — it normalizes velocity over the specimen's gauge length. For instance, ASTM D638 Type V specimens (10 mm gauge length) reach five times the strain rate of Type I specimens (50 mm) at the same test velocity.
Accurate simulations require test data that spans the strain rate range encountered in the application, ideally covering 3–5 decades of strain rate. Simply testing at one high rate is insufficient. Rate dependency affects not just yield stress but also stiffness and failure strain.
Measuring Rate-Dependent Properties
High strain rate testing is challenging due to:
- Noise and vibration, especially early in the test.
- Inertia and compliance effects from test machines.
- Extensometry difficulties at high speeds.
- The risk of masking real material behavior through data smoothing.
Clean data acquisition is essential. Properly configured servo-hydraulic machines are effective for rates from 0.01 to 100 s⁻¹, suitable for most impact simulations. Very high rates (up to 1000 s⁻¹) are achievable on servo-hydraulic high-speed tensile systems that apply a programmed displacement pulse to the specimen.
Either contact or non-contact extensometers may be used. If contact extensometers are employed, they must be lightweight. Use of crosshead displacement is discouraged due to poor resolution at small strains. High strain rate tests may benefit from methods like those proposed by Lobo and Perkins [see reference at bottom for further details] for better data capture.
Choosing Test Specimens
Specimen geometry and preparation significantly influence results.
Metals
- Overheating during machining can alter mechanical properties.
- Specimens should ideally come from the actual part, as forming operations induce orientation that affects strength.
- Thin metal specimens are particularly sensitive to heat-affected zones.
Plastics
- Unfilled polymers can be injection molded or machined. However, materials with high melt elasticity (e.g., blow molding grades) are best machined from formed parts to avoid flow-induced orientation.
- Fiber-filled materials need wide gauge sections to include enough intact fibers. Narrow specimens may not reflect true material behavior.
- Orientation effects and non-uniform properties in molded parts introduce variability. Ideally, all specimens should be sampled from the same part region to reduce scatter.
Polymers also show strong temperature effects on ductility and strength, in contrast to metals. However, combined temperature-rate models are still under development, so testing must be performed at the temperatures of interest.
Modeling Rate Dependency
FEA software models rate dependency through:
- Scaling of a quasi-static curve using:
- Tables of scale factors
- Strain rate equations (e.g., Cowper-Symonds, Eyring)
- Interpolating between measured curves at different strain rates.
Key Evaluation Steps:
- Yield strength vs. log strain rate: Many plastics follow Eyring behavior (linear on a semi-log plot), while metals often follow Cowper-Symonds (nonlinear).
- Modulus: If the modulus is rate-independent, implementation is easier. If modulus increases with rate (common in filled materials), software support may be limited.
- Curve shape: Analyze how the stress-strain curve changes with rate — particularly post-yield behavior. If consistent, a quasi-static reference curve can be scaled. If not, interpolation of full curves is preferred.
- Ductile-to-brittle transition: Common in polymers like PP and PE at high strain rates and must be considered in failure modeling.
Point Selection and Curve Fitting
Simulations work best with a reduced, clean set of points. All post-yield data must be presented as true stress vs. plastic strain, per standard material modeling practices.
For polymers, which often lack clearly defined yield points and exhibit nonlinear elasticity, the initial yield point must be carefully estimated. A common method is to:
- Determine a pre-yield modulus from a few initial points.
- Define the post-yield slope, and
- Project the intersection with the modulus line to find a logical "yield" point.
This avoids selecting a post-yield slope too similar to the initial modulus, which can cause simulation instabilities.
In negative slope regions (post-necking), fictive data points with zero or rising slopes may be required to ensure stability and accurate failure modeling. Digital Image Correlation (DIC) has shown that apparent negative slopes may simply reflect strain averaging outside the neck region.
Failure Definition and Rate Dependency
Many FEA models allow for a single failure strain or stress input. This works well only when failure strain is not strain-rate dependent. When it is, selecting the value at the highest relevant strain rate is usually best. Advanced failure models have been developed that incorporate multi-mode failure mechanisms.
Rate Dependency in Metals
Metals deform primarily via dislocation glide, not viscous flow. Thus, rate effects in metals are:
- Moderate at room temperature.
- More pronounced at elevated temperatures approaching transition points.
- Yield stress may increase 10x over 5 decades of strain rate.
- Modulus is rate-independent.
Consequently, simple rate scaling models are effective for metals, and modeling is generally straightforward.
Rate Dependency in Polymers
Polymers show strong nonlinear, rate-dependent behavior:
- High plastic flow at low strain rates can cause simulation issues (e.g., element distortion).
- At high strain rates, polymers often become brittle, which simplifies simulation but alters failure mode.
- Polymers require viscoplastic formulations to capture both deformation and distribution of stress.
Common failure modes like crazing (internal voids) are not well captured by typical material models. New, complex models are being developed but are not yet widely adopted.
Fiber-Filled and Brittle Polymers
These materials pose modeling challenges due to:
- Strong modulus rate dependency.
- Very low strains to failure (≈2%).
- Immediate divergence in stress-strain behavior at different rates.
Because failure occurs early and rapidly, it is difficult to capture true mechanical response. Linear or bilinear models, despite being simplified, often offer better accuracy than more complex formulations due to better curve-fitting over the short strain range.
Rate Dependency of Foams
Foams, including crushable foams (e.g., EPS) and elastomeric foams (e.g., PU), are highly rate dependent and are used mainly for energy absorption.
Foam Characteristics
- Rate effects cause two-directional scaling: with increasing strain rate, stress increases and strain decreases.
- Stress-strain curves at various strain rates must be used for modeling; scaling equations are insufficient.
Foam Testing
- Use 5 strain rates, typically ranging from quasi-static to high-speed drop tests.
- Ensure constant-speed conditions, especially at high rates.
- Data beyond the constant-speed range must be extrapolated using a hyperbolic sine function.
- Crossover, due to noise, of stress-strain curves for different strain rates must be avoided via data smoothing.
Unloading and Recovery
- Some models allow input of unloading curves, useful for simulating hysteresis and damage.
- High-compression applications may require the extension of compressive curves into the tensile region to avoid instabilities.
Foam Model Extensions
- Viscoelastic foam models combine rate dependency with Prony series for time-based recovery.
- Hyperfoam models (e.g., Ogden-based) paired with viscoelastic models enable simulations of large deformations and time effects in elastomeric foams.
Conclusion
Rate dependency is a critical consideration in simulating real-world mechanical behavior, particularly for impact, crash, or dynamic loading conditions. The strain rate, rather than simply impact speed, dictates how materials respond during deformation.
Summary of Key Takeaways
- Material testing must span multiple decades of strain rate to provide valid models.
- Clean, accurate data is essential — noise and test artifact management are crucial.
- Polymers exhibit complex rate behavior and require careful model selection, especially when modulus or curve shape changes with rate.
- Metals are simpler to model due to more linear behavior.
- Foams and fiber-filled materials demand customized approaches, often using interpolated curve libraries.
- Failure modeling, particularly in polymers, remains an evolving field with new approaches under development.
The rate dependency of a material not only alters stiffness and strength but also impacts the failure mode and the accuracy of simulations. Understanding how to test, interpret, and implement this behavior is fundamental to effective product design and material characterization in CAE.
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.10.
