Phase-field modeling of crack propagation in heterogeneous materials with multiple crack order parameters

Schöller, Lukas; Schneider, Daniel; Herrmann, Christoph S.; Prahs, Andreas; Nestler, Britta

doi:10.1016/j.cma.2022.114965

Cited by 26 publications

(10 citation statements)

References 67 publications

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“…Schöller et al [1] proposed a MCOP model for fracture in heterogeneous materials. Despite the improvement in the qualitative and quantitative prediction of crack paths for such systems, the model has some limitations.…”

Section: Discussionmentioning

confidence: 99%

“…is introduced to track the local damage to a material point in respect to the volume of the corresponding subregion [1,21] and therefore representing the sharp crack surfaces S α c . Based on these sets of order parameters, the free energy of a heterogeneous body is approximated by the functional…”

Section: Multi Crack Order Parameter Phase-field Modelmentioning

confidence: 99%

“…with the displacement vector u, is unknown. Schöller et al [1] used a Voigt-Taylor homogenization scheme, for which ε α = ε ∀α = 1, . .…”

Section: Mechanical Jump Conditionsmentioning

confidence: 99%

“…[10][11][12]. However, as recently discussed by Henry [13] and Schöller et al [1], these approaches have some limitations as they can lead to nonphysical fracture behavior. Schöller et al [1] presented an alternative approach for a phase-field crack propagation model in heterogeneous materials by introducing multi-crack order parameters (MCOP).…”

Section: Introductionmentioning

confidence: 99%

“…However, most of these crack propagation models are for homogeneous materials, and there exist only a few approaches for heterogeneous systems. Recently, Schöller et al [1] presented a novel phase-field model for multiphase materials, e.g. composites, based on multi-crack crack order parameters.…”

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confidence: 99%

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Phase‐field modeling of crack propagation based on multi‐crack order parameters considering mechanical jump conditions

Schöller

Schneider

Prahs

et al. 2023

Proc Appl Math and Mech

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The phase field method is commonly used for the crack propagation modeling in modern material science, as they allow for an implicit tracking of the crack surface. However, most of these crack propagation models are for homogeneous materials, and there exist only a few approaches for heterogeneous systems. Recently, Schöller et al. [1] presented a novel phase‐field model for multiphase materials, e.g. composites, based on multi‐crack crack order parameters. Despite the quantitative advantages of the model, it is based on a simple scheme for the underlying homogenization problem. In this work, a more advanced homogenization scheme based on mechanical jump condition is applied to the model. Consideration of these jump conditions yields phase‐specific stresses and strains. Therefore, the mechanical driving force for crack propagation can be modeled as more independent of the elastic properties of other physical regions. Volume elements of a fiber reinforced polymer are used to demonstrate the limitations of the simple scheme, as well the improvement if considering mechanical jump conditions. Thereby, the contrast in the crack resistance of the two materials is varied. It is shown that the simple linear interpolation does not lead to reasonable crack paths for contrary contrasts of elastic modulus and crack resistance. Taking into account the mechanical jump conditions instead yields still reasonable results. For both the final crack paths and the stress‐strain curves of the system, the novel model is less sensitive to a change in fiber crack resistance. While the result of the simple scheme depend on the selected fiber crack resistance, although failure of the matrix is expected.

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Section: Discussionmentioning

confidence: 99%

Section: Multi Crack Order Parameter Phase-field Modelmentioning

confidence: 99%

“…with the displacement vector u, is unknown. Schöller et al [1] used a Voigt-Taylor homogenization scheme, for which ε α = ε ∀α = 1, . .…”

Section: Mechanical Jump Conditionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Phase‐field modeling of crack propagation based on multi‐crack order parameters considering mechanical jump conditions

Schöller

Schneider

Prahs

et al. 2023

Proc Appl Math and Mech

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Microstructure evolution accounting for crystal plasticity in the context of the multiphase-field method

Kannenberg,

Schöller,

Prahs

et al. 2023

Comput Mech

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The role of grain boundaries (GBs) and especially the migration of GBs is of utmost importance in regard of the overall mechanical behavior of polycrystals. By implementing a crystal plasticity (CP) theory in a multiphase-field method, where GBs are considered as diffuse interfaces of finite thickness, numerically costly tracking of migrating GBs, present during phase transformation processes, can be avoided. In this work, the implementation of the constitutive material behavior within the diffuse interface region, considers phase-specific plastic fields and the jump condition approach accounting for CP. Moreover, a coupling is considered in which the phase-field evolution and the balance of linear momentum are solved in each time step. The application of the model is extended to evolving phases and moving interfaces and approaches to strain inheritance are proposed. The impact of driving forces on the phase-field evolution arising from plastic deformation is discussed. To this end, the shape evolution of an inclusion is investigated. The resulting equilibrium shapes depend on the anisotropic plastic deformation and are illustrated and examined. Subsequently, evolving phases are studied in the context of static recrystallization (SRX). The GB migration involved in the growth of nuclei, which are placed in a previously deformed grain structure, is investigated. For this purpose, three approaches to strain inheritance are compared and, subsequently, different grain structures and distributions of nuclei are considered. It is shown, how the revisited method contributes to a simulation of SRX.

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Crack nucleation in heterogeneous bars: h- and p-FEM of a phase field model

Levy,

Vicentini,

Yosibash

2024

Comput Mech

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Failure initiation and subsequent crack trajectory in heterogeneous materials, such as functionally graded materials and bones, are yet insufficiently addressed. The AT1 phase field model (PFM) is investigated herein in a 1D setting, imposing challenges and opportunities when discretized by h- and p-finite element (FE) methods. We derive explicit PFM solutions to a heterogeneous bar in tension considering heterogeneous E(x) and $$G_{Ic}(x)$$ G Ic ( x ) , necessary for verification of the FE approximations. $$G_{Ic}(x)$$ G Ic ( x ) corrections accounting for the element size at the damage zone in h-FEMs are suggested to account for the peak stress underestimation. p-FEMs do not require any such corrections. We also derive and validate penalty coefficient for heterogeneous domains to enforce damage positivity and irreversibility via penalization. Numerical examples are provided, demonstrating that p-FEMs exhibit faster convergence rates comparing to classical h-FEMs. The new insights are encouraging towards p-FEM discretization in a 3D setting to allow an accurate prediction of failure initiation in human bones.

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Phase-field modeling of crack propagation in heterogeneous materials with multiple crack order parameters

Cited by 26 publications

References 67 publications

Phase‐field modeling of crack propagation based on multi‐crack order parameters considering mechanical jump conditions

Phase‐field modeling of crack propagation based on multi‐crack order parameters considering mechanical jump conditions

Microstructure evolution accounting for crystal plasticity in the context of the multiphase-field method

Crack nucleation in heterogeneous bars: h- and p-FEM of a phase field model

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