Simulation of dislocation dynamics enables researchers and scientists to explore the plastic behavior of crystalline materials under loading. Analytic solutions for the stress field due to a linear dislocation segment near a free surface are case-specific, e.g. dealing with either a horizontal segment or a vertical segment, and therefore hard to implement in time-dependent dislocation dynamics simulations as different dislocation segments could be differently oriented. This article presents a generalized numerical framework to find the stress field beneath a free surface due to the presence of a dislocation segment. The framework can be expanded to non-flat surfaces. Also, three-dimensional discrete dislocation dynamics simulations are performed here, which clearly show the effect of free surfaces on the flow stress of a material.

Fe–Co–2V (Hiperco®2 equivalent) is a soft ferromagnetic material that is commonly used for electrical components that require robust magnetic performance. Despite the excellent magnetic properties of Fe–Co–2V, it often exhibits low strength, ductility, and workability due to an ordered B2 microstructure. The mechanical properties exhibit considerable dependency on grain size and degree of order, which are influenced by processing methods. A thorough understanding of Fe–Co–2V’s fatigue performance is required to predict mechanical reliability under operating loads; however, limited fatigue data currently exist for Fe–Co alloys. This work characterizes the fatigue properties of wrought Fe–Co–2V through strain-controlled fatigue testing and fractography. Young’s modulus, ultimate strength, and yield stress were determined through monotonic tension tests. The fatigue behavior was quantified using fully reversed, strain-controlled fatigue testing for applied strain amplitudes ranging from 0.10% to 1.00%. Subsequently, the Coffin–Manson strain-life curve was fit to the experimental data. Failure mechanisms were investigated through fractography with a scanning electron microscope. Inspection of the failure surfaces revealed that crack initiation occurred at defects located on or near the specimen surface with a localized region of crack propagation prior to the transgranular cleavage fracture. Additionally, two material models were calibrated from the experimental static and cyclic experimental testing. The characterization of the fatigue behavior of wrought Fe–Co–2V presented herein will aid in the fatigue analysis of Fe–Co–2V components and the development of analytical fatigue modeling methodologies.

Research problems are often modeled using sets of linear equations and presented as matrix equations. Eigenvalues and eigenvectors of those coupling matrices provide vital information about the dynamics/flow of the problems and so needs to be calculated accurately. Analytical solutions are advantageous over numerical solutions because numerical solutions are approximate in nature, whereas analytical solutions are exact. In many engineering problems, the dimension of the problem matrix is 3 and the matrix is symmetric. In this paper, the theory behind finding eigenvalues and eigenvectors for order 3×3 symmetric matrices is presented. This is followed by the development of analytical solutions for the eigenvalues and eigenvectors, depending on patterns of the sparsity of the matrix. The developed solutions are tested against some examples with numerical solutions.

Plastic deformation in metals is dominated by the interactions among dislocations and other defects inside the crystal. A large number of dislocation multipoles (dipoles, tripoles, quadrupoles, etc.) can form during plastic deformation. Depending on the relative position and the orientation of the dislocations, interactions in and between multipoles can change the elastoplastic properties of a material. The authors of this article investigate the effect of dislocation multipoles on the elastoplastic properties of a material. This is performed analytically under different multipole configurations (i.e., the distance between active glide planes and the signs of the dislocations) as well as using a three-dimensional discrete dislocation dynamics (DDD) code. The simulations show that multipoles exhibit a hardening/softening effect when the sign of the dislocations involved is the same, and a hardening effect only when the dislocations are of opposite sign to nearby ones. The distance between the two neighboring dislocations was also affecting the proportional limit (PL) for the material. Such hardening or flow stress (FS) results, as in this study, can be incorporated into larger-scale modeling work.