Thermal-conductivity degradation across cracks in coupled thermo-mechanical systems modeled by the phase-field fracture method

Svolos, Lampros; Bronkhorst, Curt A.; Waisman, Haim

doi:10.1016/j.jmps.2019.103861

Cited by 63 publications

(8 citation statements)

References 51 publications

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“…The influence of crack on the thermal field was also studied, specifically the heat conduction. Svolos et al [47] proposed a thermal-conductivity degradation function derived from a novel micromechanics analytical approach using spherical harmonics, and showed that the thermal conductivity across cracks must be degraded to satisfy crack Neumann boundary conditions. Furthermore, they proposed a new anisotropic approach [48] in which thermal conductivity, which depends on the phase-field gradient, is degraded solely across the crack.…”

Section: Phase-field Fracture Modelmentioning

confidence: 99%

“…In the above relation, k 0 is the thermal conductivity of the undamaged material, and g(d) is a thermal degradation function which ensures that no heat flux exists across the crack. Though there are other forms of thermal degradation proposed in the work of [47,48], an isotropic conductivity degradation g(d) = (1 − d) 2 + ξ is adopted here, where ξ is a small number for numerical and physical purposes. Substituting Eq.…”

Section: Damaged Informed Heat Conductionmentioning

confidence: 99%

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A thermo-mechanical phase-field fracture model: application to hot cracking simulations in additive manufacturing

Ruan¹,

Rezaei²,

Yang³

et al. 2022

Preprint

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Thermal fracture is prevalent in many engineering problems and is one of the most devastating defects in metal additive manufacturing. Due to the interactive underlying physics involved, the computational simulation of such a process is challenging. In this work, we propose a thermo-mechanical phase-field fracture model, which is based on a thermodynamically consistent derivation. The influence of different coupling terms such as damage-informed thermomechanics and heat conduction and temperature-dependent fracture properties, as well as different phase-field fracture formulations, are discussed. Finally, the model is implemented in the finite element method and applied to simulate the hot cracking in additive manufacturing. Thereby not only the thermal strain but also the solidification shrinkage are considered. As for thermal history, various predicted thermal profiles, including analytical solution and numerical thermal temperature profile around the melting pool, are regarded, whereas the latter includes the influence of different process parameters. The studies reveal that the solidification shrinkage strain takes a dominant role in the formation of the circumferential crack, while the temperature gradient is mostly responsible for the central crack. Process parameter study demonstrates further that a higher laser power and slower scanning speed are favorable for keyhole mode hot cracking while a lower laser power and quicker scanning speed tend to form the conduction mode cracking. The numerical predictions of the hot cracking patterns are in good agreement with similar experimental observations, showing the capability of the model for further studies.

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Section: Phase-field Fracture Modelmentioning

confidence: 99%

Section: Damaged Informed Heat Conductionmentioning

confidence: 99%

A thermo-mechanical phase-field fracture model: application to hot cracking simulations in additive manufacturing

Ruan¹,

Rezaei²,

Yang³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…By considering cracks as localized changes in a phase field variable, phase field fracture requires no explicit tracking of the crack front, and can thus simulate arbitrarily complex crack geometries. Phase field fracture is straightforward to generalize to different physical scenarios, with variants for dynamic [8,9] and quasi-static [1] fracture and extensions that include plasticity [4,10] and a variety of other multi-physics phenomena [6,11,12]. The development of phase field fracture over the last 20 years has even lead to a variety of different models for even the relatively simple case of quasistatic brittle fracture (see reviews [2,3]).…”

Section: Introductionmentioning

confidence: 99%

Crack-path selection in phase-field models for brittle fracture

Andrews¹,

Pastewka²

2022

Preprint

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This work presents a critical overview of the effects of different aspects of model formulation on crack path selection in quasi-static phase field fracture. We consider different evolution methods, mechanics formulations, fracture dissipation energy formulations, and forms of the irreversibility condition. The different model variants are implemented with common numerical methods based on staggered solution of the phase-field and mechanics sub-problems via FFT-based solvers. These methods mix standard approaches with novel elements, such as the use of bound-constrained conjugate gradients for the phase field sub-problem and a heuristic method for near-equilibrium evolution. We examine differences in crack paths between model variants in simple model systems and microstructures with randomly heterogeneous Young's modulus. Our results indicate that near-equilibrium evolution methods are preferable for quasi-static fracture of heterogeneous microstructures compared to minimization and time-dependent methods. In examining mechanics formulations, we find distinct effects of crack driving force and the model for contact implicit in phase field fracture. Our results favor the use of a strain-spectral decomposition for the crack driving force but not the contact model. Irreversibility condition and fracture dissipation energy formulation were also found to affect crack path selection, but systematic effects were difficult to deduce due to the overall sensitivity of crack selection within the heterogeneous microstructures. Our findings support the use of the AT1 model over the AT2 model and irreversibility of the phase field within a crack set rather than the entire domain. Sensitivity to these differences in formulation was reduced but not eliminated by reducing the crack width parameter relative to the size scale of the random microstructures.

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“…An alternative approach is to use the phase‐field method, 24 which is closely related to nonlocal gradient‐type damage mechanics and has been applied to describe fracture failure of porous media 63,64 . However, while the phase‐field method has some attractive numerical features, which could be used herein, the degradation functions used in these methods lack any physical meaning as opposed to damage laws used in this work 65 . Detailed comparison between phase field and nonlocal gradient‐type damage approaches can be found elsewhere 66 .…”

Section: Introductionmentioning

confidence: 99%

Dynamic soil consolidation model using a nonlocal continuum poroelastic damage approach

Chen

Mobasher

Waisman

2021

Num Anal Meth Geomechanics

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We present a novel dynamic poroelastic model for soil consolidation in an isotropic homogeneous fluid saturated porous media. A nonlocal integral‐type continuum damage formulation is applied to describe the damage evolution under dynamic excitations, in which a bilinear damage law is assumed. The governing equations are obtained by considering the conservation of momentum and mass balance for the solid–fluid mixtures, in which the fluid flow obeys Darcy's seepage law in the entire domain. The numerical solution of the fully coupled problem is achieved via a mixed FEM displacement–pressure false(u−pfalse)$(u-p)$ element formulation. The mechanical equilibrium equations are evolved in time using a Newmark method and the resulting nonlinear system is solved via a Newton–Raphson method. Consistent linearization is then used to obtain the block Jacobian matrix analytically and the linear system is solved monolithically at each time step. Several numerical results are presented to study soil consolidation problems under harmonic excitations. We investigate the time‐dependence response of the skeleton displacement, pressure, and damage evolution. In addition, the examples demonstrate that the nonlocal integral‐type damage model can effectively overcome mesh dependence and yield smooth behavior.

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Thermal-conductivity degradation across cracks in coupled thermo-mechanical systems modeled by the phase-field fracture method

Cited by 63 publications

References 51 publications

A thermo-mechanical phase-field fracture model: application to hot cracking simulations in additive manufacturing

A thermo-mechanical phase-field fracture model: application to hot cracking simulations in additive manufacturing

Crack-path selection in phase-field models for brittle fracture

Dynamic soil consolidation model using a nonlocal continuum poroelastic damage approach

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