About Eigenstrain
Residual stresses in mechanical parts are stresses that exist in the absence of externally applied loads. Almost all manufacturing processes, including additive manufacturing, introduce residual stresses into mechanical parts. Residual stresses are sometimes introduced intentionally to improve the in-service response, such as in prestressed concrete slabs used in bridge construction. However, manufacturers often try to minimize residual stresses because they can cause fracture during the manufacturing process, lead to unwanted distortions, and significantly impact fatigue behavior. Three primary classes of manufacturing effects lead to residual stresses:
- Mechanical (for example, inelastic deformation);
- Thermal (for example, nonuniform thermal expansion or incompatible thermal strains generated during melting and solidification in the process zone); and
- Changes in material microstructure (for example, phase transformations).
Eigenstrain (also referred to as inherent strain, assumed strain, or "stress-free" strain) is an engineering concept used to account for all sources of inelastic deformation that lead to residual stresses and distortions in manufactured components. Thermal strains are a subset of eigenstrains.
In a linear elastic deformation, the stress induced by an eigenstrain can be represented as
where
σ is the Cauchy stress;
Del is the elastic matrix;
ε is the total strain;
ε* is the eigenstrain; and
εel is the elastic strain.
Using constitutive equations (such as the one shown above) eigenstrains can be used to compute residual stresses coming from mechanical, thermal, and microstructural sources.
An eigenstrain in three dimensions is represented as a standard strain tensor with six components:
The components of the eigenstrain tensor are functions of many factors, including material properties, manufacturing processes, and thermal history. Various methods can be used to determine appropriate eigenstrains for a given process:
- Destructive and nondestructive tests of manufactured parts.
- Numerical simulation.
- Analytical formulas for simple scenarios.
Once an appropriate eigenstrain field has been determined, it can be applied in an eigenstrain analysis to predict the distortions and residual stresses in an additive manufactured part.