Strain localization in polycrystalline material with second phase particles: Numerical modeling with application to ice mixtures

Abstract

We use a centimeter-scale 2-D numerical model to investigate the effect of the presence of a second phase with various volume percent, shape, and orientation on strain localization in a viscoelastic matrix. In addition, the evolution of bulk rheological behavior of aggregates during uniaxial compression is analyzed. The rheological effect of dynamic recrystallization processes in the matrix is reproduced by viscous strain softening. We show that the presence of hard particles strengthens the aggregate, but also causes strain localization and the formation of ductile shear zones in the matrix. The presence of soft particles weakens the aggregate, while strain localizes within the particles and matrix between particles. The shape and the orientation of second phases control the orientation, geometry, and connectivity of ductile shear zones. We propose an analytical scaling method that translates the bulk stress measurements of our 2-D simulations to 3-D experiments. Comparing our model to the laboratory uniaxial compression experiments on ice cylinders with hard second phases allows the analysis of transient and steady-state strain distribution in ice matrix, and strain partitioning between ice and second phases through empirical calibration of viscous softening parameters. We find that the ice matrix in two-phase aggregates accommodates more strain than the applied bulk strain, while at faster strain rates some of the load is transferred into hard particles. Our study illustrates that dynamic recrystallization processes in the matrix are markedly influenced by the presence of a second phase.

Strain Localization and Weakening Processes in Viscously Deforming Rocks: Numerical Modeling Based on Laboratory Torsion Experiments

“…The software was originally designed to investigate lithospheric‐scale processes and has since been applied in divergent (Brune, ; Brune et al, , , , , ; Brune & Autin, ; Clift et al, ; Heine & Brune, ; Koopmann et al, ), convergent (Ballato et al, ; Duesterhoeft et al, ; Quinteros et al, ; Quinteros & Sobolev, ), and transform (Brune, ; Popov et al, ) plate boundary settings. Recently, however, its scope has been extended with the aim to investigate localization processes on the centimeter scale (Cyprych et al, ).…”

“…To account for the rheological weakening mechanisms operating in rocks at elevated temperatures and pressures, we implement the function A ε that captures progressive weakening. The strain rate in each element is increased by this factor A ε depending on the actual viscous strain ε of the element: The threshold values ε 1 and ε 2 depend either on (1) accumulated finite viscous strain (see Cyprych et al, ) or (2) deformation work per element volume W def defined as with ε visc as the viscous component of finite strain, which is computed by integrating the second invariant of the deviatoric viscous strain rate tensor with respect to time. For all ε < ε 1 the factor A ε is 1.…”

“…For example, during lithospheric extension the inherited mechanical structure exerts a strong control on rift geometry and architecture (Duretz et al, ). Material heterogeneities significantly impact strain localization: (1) hard inclusions produce stress concentrations inside a homogeneous matrix (Kenkmann & Dresen, ) and (2) weak inclusions localize strain in turn producing stress concentrations at the inclusion matrix interface (Cyprych et al, ). Jammes et al () identified three end‐member types of shear zones: (1) localized, (2) localized anastomosing, and (3) delocalized shear zone that depend on the proportion of strong and weak phase and the strength ratio.…”

“…Other modeling studies focused on the effect of rheological weakening and hardening mechanisms. Weakening mechanisms have been formulated as a function of strain (Cyprych et al, ; Mazzotti & Gueydan, ), stress (Gardner et al, ), and deformation work or grain size in combination with grain size‐dependent flow laws (e.g., Bercovici & Ricard, ; Cross et al, ; Herwegh et al, ; Jessell et al, ). However, all these formulations have been shown to strongly influence the localization behavior in numerical models.…”

Controls of inherited lithospheric heterogeneity on rift linkage: Numerical and analog models of interaction between the Kenyan and Ethiopian rifts across the Turkana depression

“…The deformation of materials is accommodated via an elastoviscoplastic rheology, which self‐consistently reproduces diverse deformation processes like faulting, flexure, and lower crustal flow. SLIM3D has been extensively benchmarked and applied to model lithospheric‐scale processes in divergent [ Brune et al , , ; Brune and Autin , ; Brune , ; Heine and Brune , ; Koopmann et al , ; Clift et al , ; Brune et al , , ], convergent [ Quinteros et al , ; Quinteros and Sobolev , ; Duesterhoeft et al , ], and transform [ Popov et al , ; Brune , ] plate boundaries and in a centimeter‐scale study of localization dynamics [ Cyprych et al , ].…”