Hey there! In this article, we’ll talk about material plasticity, how ANSYS uses it, and some tips for picking the right plasticity models.
What is Plasticity?
When it comes to defining a linear material model in ANSYS, you need to set the young’s modulus and poison’s ratio. But for non-linear material modeling, you also need a material plasticity model and a stress-strain curve to be included as part of the material properties. Basically, material plasticity means that the material will experience irreversible deformation once a certain stress (load) is reached.
Why is Plasticity Important in Material Modeling?
The yield strength of most metals can be determined through a tensile test in a lab. This test involves taking a specimen of the material with a known uniform cross section and applying a uniaxial tensile force to it. A stress-strain plot is generated to show the mechanical behavior of the specimen. However, determining the exact point at which yielding starts is difficult. Typically, the stress corresponding to 0.2% plastic strain is considered the yield strength, which corresponds to a stress level where yielding has already begun.
When someone talks about a material with a yield strength of 150 MPa, it means that under a uniaxial loading situation, a tensile stress of 150 MPa will cause the material to yield. But real-life loading situations are usually more complex than this. Components usually experience a combined loading situation involving tensile forces, bending moments, and torques.
How do we figure out what kind of stress causes materials to yield when they’re under multiaxial loading, and how does plasticity change as the stress increases?
To answer these questions, we need to understand plasticity modeling.
There are two main types of plasticity models: rate-independent and rate-dependent.
Rate-independent plasticity assumes that plastic strains develop immediately and are not affected by time. This is a good assumption for most engineering problems.
Rate-dependent plasticity, on the other hand, considers how plastic flows in materials depend on time or strain rate. This is used for specialized applications like thermal creep and metal forming.
Rate-independent plasticity models consist of three components:
Yield Criterion: This is a statement that defines the conditions under which yielding will occur. It can be expressed in terms of different quantities like stress state, strain state, or strain energy.
Flow Rule: This determines the direction of flow of the plastic strains. It tells us how the plastic strain increments relate to the stress increments after yielding.
Hardening Rule: This describes how plastic strain affects the strength of the material. Specifically, it predicts how the yield surface (a geometric representation of the yield criterion) changes due to plastic strain.
ANSYS offers various options for modeling plasticity, each with its own set of features. Let’s take a look at some of the most popular options.
- Bilinear Isotropic Hardening (BISO)
- Multilinear Isotropic Hardening (MISO)
- Nonlinear Isotropic Hardening (NLISO)
- Bilinear Kinematic Hardening (BKIN)
- Multilinear Kinematic Hardening (MKIN)
- Chaboche Kinematic Hardening (CHAB)
- Hill Yield Criterion (HILL)
It would be helpful to create a chart that explains some of the terms commonly used in plasticity modeling and how they relate to one another.
Yield Criteria or Hardening Rules can be described as isotropic or anisotropic. The von-Mises Yield Criterion is the standard criterion used for most plasticity models. The Hill and Chaboche models can be used to modify various aspects of isotropic and kinematic hardening models.
Isotropic vs Kinematic Hardening
Isotropic and kinematic hardening are two of the most widely used plasticity models for ductile metals. Kinematic hardening predicts a lower compressive yield strength than isotropic hardening, as shown in Figure 2. This is due to the Bauschinger effect.
Figure 2: Isotropic vs Kinematic Hardening
Figure 3 shows the hardening rules associated with isotropic and kinematic hardening. Yielding occurs when stress states (in terms of maximum and minimum principal stresses) lie outside the yield surfaces. The dashed outline represents the shift of the yield surface due to work hardening. For isotropic hardening, the yield surface expands uniformly, while for kinematic hardening, it translates as a rigid body.
Figure 3: Isotropic vs Kinematic Hardening Yield Surfaces
The terms “Bilinear” and “Multilinear” refer to the number of slopes present in the stress-strain curve. A bilinear curve has two slopes, while a multilinear curve has more than two slopes. A smooth curve generated from multiple data points is also considered multilinear. The term “Linear” refers to the linear relationship between hardening and plastic strains, as shown in Figure 3. Additionally, the yield surface can flow indefinitely without any limit to its extent.
Bilinear vs Multilinear Hardening
Linear Behavior: When we talk about linear behavior, it means that there is a direct relationship between hardening and plastic strains. As seen in Figure 3, the yield surfaces’ dilation and translation are directly proportional to the plastic strains. It also means that the yield surface can keep flowing without any limit to its extent.
Bi and Multi-Slope Behavior: When we talk about bilinear or multilinear stress-strain curves, it means that the curve has multiple slopes. Bilinear curve, for instance, consists of two slopes, while a multilinear stress-strain curve has more than two slopes. Even a smooth curve generated from multiple data points is considered multilinear.
The relationship between hardening and plastic strains is not linear
The yield surface cannot translate indefinitely in principal stress space
The behavior of the model eventually reaches perfectly plastic
Choosing the Right Plasticity Model
The choice of plasticity model depends on the type of material and the loading situation. Here are some guidelines for selecting different models:
- Isotropic Hardening: Isotropic hardening is suitable for large strain, proportional loading scenarios. Proportional loading refers to situations when the orientation of the principal stresses remains the same during the course of loading. However, it is not appropriate for cyclic loading applications.
- Voce Non-Linear Isotropic Hardening: This model is suitable for materials that show a smooth transition between the elastic and large-strain plastic regions.
- Bilinear Hardening: Bilinear hardening is suitable for relatively low strain levels (around 5-10% strain). However, it does not accurately represent actual behavior because the hardening is represented by a single tangent modulus (slope of the line for the plastic portion of the curve) that remains constant.
- Multi-Linear and Non-Linear Kinematic Hardening: These models are suitable for large strain scenarios. They represent the behavior of the material with multiple slopes in the stress-strain curve, making it more accurate.