A thermodynamics-based variational method is developed to establish the equations of motion for three-dimensional (3D) interacting dislocation loops. The approach is appropriate for investigations of plastic deformation at the mesoscopic scale by direct numerical simulations. A fast sum technique for determination of elastic field variables of dislocation ensembles is utilized to calculate forces acting on generalized coordinates of arbitrarily curved loop segments. Each dislocation segment is represented by a parametric space curve of specified shape functions and associated degrees of freedom. Kinetic equations for the time evolution of generalized coordinates are derived for general 3D climb/glide motion of curved dislocation loops. It is shown that the evolution equations for the position $\left(\mathbf{P}\right),$ tangent $\left(\mathbf{T}\right),$ and normal $\left(\mathbf{N}\right)$ vectors at segment nodes are sufficient to describe general 3D dislocation motion. When crystal structure constraints are invoked, only two degrees of freedom per node are adequate for constrained glide motion. A selected number of applications are given for: (1) adaptive node generation on interacting segments, (2) variable time-step determination for integration of the equations of motion, (3) dislocation generation by the Frank-Read mechanism in fcc, bcc, and dc crystals, (4) loop-loop deformation and interaction, and (5) formation of dislocation junctions.

The elastic field of complex shape ensembles of dislocation loops is developed as an essential ingredient in the dislocation dynamics method for computer simulation of mesoscopic plastic deformation. Dislocation ensembles are sorted into individual loops, which are then divided into segments represented as parametrized space curves. Numerical solutions are presented as fast numerical sums for relevant elastic field variables (i.e., displacement, strain, stress, force, self-energy, and interaction energy). Gaussian numerical quadratures are utilized to solve for field equations of linear elasticity in an infinite isotropic elastic medium. The accuracy of the method is verified by comparison of numerical results to analytical solutions for typical prismatic and slip dislocation loops. The method is shown to be highly accurate, computationally efficient, and numerically convergent as the number of segments and quadrature points are increased on each loop. Several examples of method applications to calculations of the elastic field of simple and complex loop geometries are given in infinite crystals. The effect of crystal surfaces on the redistribution of the elastic field is demonstrated by superposition of a finite-element image force field on the computed results.

This paper conducts a quantitative analysis of microstructural damage evolution of concrete materials under freeze-thaw action using three-dimensional X-ray computed tomography. The study employs two resolution-scales to evaluate concrete samples under various cycles of freeze-thaw action. The three-dimensional microstructural damage characterization, pore network (porosity, pore size, and pore distribution) as well as the defects in the aggregates are specifically investigated. The microstructures of concrete under different freeze-thaw action show that the interfacial transition zone is most likely to be damaged first under frost attack. Furthermore, the freeze-thaw action deteriorates not only the interfacial transition zone but also cement matrix and aggregates. The impact of freeze-thaw cycles is notable on the internal micro-pores and micro-cracks of the concrete. More pores and cracks can be nucleated during the freeze-thaw action, and further accumulate and grow in the paste and aggregates, eventually leading to final failure of concrete materials. As demonstrated in this study, three-dimensional X-ray computed tomography is capable of acquiring microstructures of concrete and revealing existence of internal pores and cracks in different phases of concrete, and more effective to characterize accumulated damage of concrete due to freeze-thaw action.

Concrete structures in cold regions are exposed to cyclic freezing and thawing environment, leading to degraded mechanical and fracture properties of concrete due to microstructural damage. While the X-ray micro-/nano-computed tomography technology has been implemented to directly observe concrete microstructure and characterize local damage in recent years, the freeze-thawed damage evolution processes and its effect on overall mechanical performance are not well understood. In this paper, the X-ray nano-computed tomography technology and micro-scale cohesive zone model are combined to quantitatively investigate microstructural damage evolution and its effect on fracture behavior of freeze-thawed concrete samples in three-point bending tests. A two-level micro-to-macro scale finite element model is developed based on computed tomography microstructural images with microcracks due to freeze-thaw cycles. The macroscopic load–deflection curves and fracture energies are simulated and compared favorably with experimental results. Simulation results demonstrate that microcracks caused by freeze-thaw actions are the primary reason for degradation of concrete mechanical properties. Fracture behaviors of frost-damaged concrete with different mortar and interfacial transition zone strength and fracture constants are also simulated and discussed. The combined X-ray nano-computed tomography technology and cohesive zone model proposed is effective in characterizing fracture behavior of concrete and capturing freeze-thaw cycle-induced microstructural damage evolution and its effect on fracture process of concrete.

Plastic instability associated with formation of narrow flow channels results from dislocation pinning–unpinning by defect clusters. We investigate the dynamics of dislocation interaction with radiation-induced defect clusters, and specifically with, firstly, sessile self-interstitial atom clusters in dislocation decorations and, secondly, stacking-fault tetrahedra (SFTs) in the matrix. It is shown that the critical stress to free trapped dislocations from pinning atmospheres can be a factor of two smaller than values obtained on the basis of rigid dislocation interactions. The unpinning mechanism is a consequence of the growth of morphological instabilities on the dislocation line. Dislocation sources are activated in spatial regions of low SFT density, where their destruction by glide dislocations leads to subsequent growth of localized plasticity in dislocation channels. We show that removal of SFTs is associated with simultaneous dislocation glide and climb. Jogs of atomic dimensions are formed when a fraction of SFT vacancies are absorbed by pipe diffusion. The width of a flow channel is explained in terms of two length scales: the size of an individual SFT, and the dislocation source-to-boundary distance (d of the order of micrometres). While dislocation segments climb by a few atomic planes with each SFT destruction event, d determines the total number of such events. Numerically computed channel widths (about 70–150nm), and the magnitude of radiation hardening in copper are consistent with experimental observations.