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Micromechanically motivated finite-strain phase-field fracture model to investigate damage in crosslinked elastomers

S. P. Josyula, M. Brede, O. Hesebeck, K. Koschek, W. Possart, A. Wulf, B. Zimmer, S. Diebels

TL;DR

The paper develops a micromechanically grounded, finite-strain viscoelastic model for crosslinked elastomers and couples it to a phase-field fracture description. By incorporating a statistical distribution of chain lengths through a Wesslau-like formulation and a Maxwell-element network, it derives a fracture energy $E_c$ from chain-network statistics and degrades stored energy via a second-order phase-field degradation function. Parameters are identified through uniaxial tensile tests at elevated temperature using a Nelder–Mead search, and the coupled model is validated against tear tests on angular specimens per DIN ISO 34-1, demonstrating robust prediction of crack initiation and propagation. The work provides a physics-based, numerically tractable framework for predicting damage in polyurethane adhesives under large deformations, with potential for design optimization of crosslinked elastomeric bonds.

Abstract

A micromechanically motivated phase-field damage model is proposed to investigate the fracture behaviour in crosslinked polyurethane adhesive. The crosslinked polyurethane adhesive typically show viscoelastic behaviour with geometric nonlinearity. The finite-strain viscoelastic behaviour is modelled using a micromechanical network model considering shorter and longer chain length distribution. The micromechanical viscoelastic network model also consider the softening due to breakage/debonding of the short chains with increase in deformation. The micromechanical model is coupled with the phase-field damage model to investigate the crack initiation and propagation. Critical energy release rate is needed as a material property to solve phase-field equation. The energy release rate is formulated based on the polymer chain network. The numerical investigation is performed using finite element method. The force-displacement curves from the numerical analysis and experiments are compared to validate the proposed material model.

Micromechanically motivated finite-strain phase-field fracture model to investigate damage in crosslinked elastomers

TL;DR

The paper develops a micromechanically grounded, finite-strain viscoelastic model for crosslinked elastomers and couples it to a phase-field fracture description. By incorporating a statistical distribution of chain lengths through a Wesslau-like formulation and a Maxwell-element network, it derives a fracture energy from chain-network statistics and degrades stored energy via a second-order phase-field degradation function. Parameters are identified through uniaxial tensile tests at elevated temperature using a Nelder–Mead search, and the coupled model is validated against tear tests on angular specimens per DIN ISO 34-1, demonstrating robust prediction of crack initiation and propagation. The work provides a physics-based, numerically tractable framework for predicting damage in polyurethane adhesives under large deformations, with potential for design optimization of crosslinked elastomeric bonds.

Abstract

A micromechanically motivated phase-field damage model is proposed to investigate the fracture behaviour in crosslinked polyurethane adhesive. The crosslinked polyurethane adhesive typically show viscoelastic behaviour with geometric nonlinearity. The finite-strain viscoelastic behaviour is modelled using a micromechanical network model considering shorter and longer chain length distribution. The micromechanical viscoelastic network model also consider the softening due to breakage/debonding of the short chains with increase in deformation. The micromechanical model is coupled with the phase-field damage model to investigate the crack initiation and propagation. Critical energy release rate is needed as a material property to solve phase-field equation. The energy release rate is formulated based on the polymer chain network. The numerical investigation is performed using finite element method. The force-displacement curves from the numerical analysis and experiments are compared to validate the proposed material model.
Paper Structure (16 sections, 71 equations, 8 figures, 1 table)

This paper contains 16 sections, 71 equations, 8 figures, 1 table.

Table of Contents

  1. Introduction
  2. Constitutive model for network viscoelasticity
  3. Micromechanically motivated polymer network model
  4. Micromechanical network viscoelastic material model
  5. Kinematics of finite-strain deformation
  6. Variational approach for phase-field fracture
  7. Regularization of phase-field formulation
  8. Degradation function
  9. Micromechanically motivated fracture energy
  10. Variational approach in solving phase-field damage
  11. Boundary conditions
  12. Numerical implementation
  13. Finite element implementation of variational principle
  14. Investigation of phase-field fracture
  15. Conclusion
  16. ...and 1 more sections

Figures (8)

  • Figure 1: Rheological model of the viscoelasticity with $n$ Maxwell elements.
  • Figure 2: Tailored tensile test samples with a necked cross-section at the centre of the sample: all dimensions are in millimetres
  • Figure 3: Numerical simulation and experimental data comparison of tensile test
  • Figure 4: Geometry of the angle sample based on DIN ISO 34-1: all dimensions are in millimetres
  • Figure 5: Finite element mesh of angular sample with refined mesh at the transition zone of crack propagation along the centre of the sample.
  • ...and 3 more figures