Poroelastic Effects on the Time- and Rate-Dependent Fracture of Polymer Gels

2019 ◽  
Vol 87 (3) ◽  
Author(s):  
Yalin Yu ◽  
Nikolaos Bouklas ◽  
Chad M. Landis ◽  
Rui Huang
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Cohesive Zone ◽  
Polymer Gels ◽  
Time Dependent ◽  
Crack Speed ◽  
Delayed Fracture ◽  
Solvent Diffusion ◽  
Rate Dependent

Abstract Fracture of polymer gels is often time- and rate-dependent. Subject to a constant load, a gel specimen may fracture immediately or after a delay (time-dependent, delayed fracture). When a crack grows in a gel, the fracture energy may depend on the crack speed (rate-dependent). The underlying mechanisms for the time- and rate-dependent fracture of gels could include local molecular processes, polymer viscoelasticity, and solvent diffusion coupled with deformation (poroelasticity). This paper focuses on the effects of poroelasticity. A path-independent, modified J-integral approach is adopted to define the crack-tip energy release rate as the energetic driving force for crack growth in gels, taking into account the energy dissipation by solvent diffusion. For a stationary crack, the energy release rate is time-dependent, with which delayed fracture can be predicted based on a Griffith-like fracture criterion. For steady-state crack growth in a long-strip specimen, the energy release rate is a function of the crack speed, with rate-dependent poroelastic toughening. With a poroelastic cohesive zone model, solvent diffusion within the cohesive zone leads to significantly enhanced poroelastic toughening as the crack speed increases, rendering a rate-dependent traction-separation relation. While most of the results are based on a linear poroelastic formulation, future studies may extend to nonlinear theories with large deformation. In addition to the poroelastic effects, other mechanisms such as viscoelasticity and local fracture processes should be studied to further understand the time and rate-dependent fracture of polymer gels.

Influence of Loading History on Delamination in Multilayered Beam with Creep

2021 ◽  
Vol 1046 ◽  
pp. 23-28
Author(s):  
Victor Iliev Rizov
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Strain Energy ◽  
Strain Energy Release Rate ◽  
Strain Energy Release ◽  
Time Dependent ◽  
External Loading ◽  
Loading History ◽  
Multilayered Beam

The present paper deals with an analytical study of the time-dependent delamination in a multilayered inhomogeneous cantilever beam with considering of the loading history. The multilayered beam exhibits creep behaviour that is treated by using a non-linear stress-strain-time relationship. The material properties are continuously distributed along the thickness and length of the layers. The external loading is applied in steps in order to describe the loading history. The analysis reveals that during each step of the loading, the strain energy release rate increases with time. The influences of crack length and location on the time-dependent strain energy release rate are also investigated.

Delayed Fracture of the Piezoelectric Ceramics Under Electric Fields in Three-Point Bending

2007 ◽  
Author(s):  
Fumio Narita ◽  
Yasuhide Shindo ◽  
Mitsuru Hirama
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Electric Fields ◽  
Lead Zirconate Titanate ◽  
Release Rate ◽  
Open Crack ◽  
Element Analysis ◽  
Delayed Fracture ◽  
Pzt Ceramics ◽  
Dc Electric Fields

This paper investigates experimentally and analytically the delayed fracture in lead zirconate titanate (PZT) ceramics under electromechanical loading. Delayed fracture tests were conducted on single-edge precracked-beam specimens, and time-to-failure and fracture load under different DC electric fields were obtained. Possible mechanisms for delayed fracture were also discussed by scanning electron microscope (SEM) examination of the fracture surface of the PZT ceramics. Further, a nonlinear finite element analysis was employed to calculate the energy release rate for the permeable, impermeable and open crack models, and the effects of applied DC electric fields and localized polarization switching on the energy release rate are examined.

Rate-Dependent Cohesive Zone Modeling of Unstable Crack Growth in an Epoxy Adhesive

2005 ◽  
Author(s):  
Dhaval P. Makhecha ◽  
Rakesh K. Kapania ◽  
Eric R. Johnson ◽  
David A. Dillard ◽  
George C. Jacob ◽  
...  
Keyword(s):  
Energy Release Rate ◽  
Crack Growth ◽  
Release Rate ◽  
Cohesive Zone ◽  
Compact Tension ◽  
Epoxy Adhesive ◽  
Mode I ◽  
Unstable Crack ◽  
Rate Dependent ◽  
Fracture Tests

This paper presents the development and numerical implementation of a rate dependent fracture model of an epoxy adhesive. Previous mode I fracture tests conducted under quasistatic, displacement controlled loading of an aluminum double cantilever beam (DCB) bonded with the epoxy exhibited unstable crack growth in the adhesive. Results from mode I fracture tests of compact tension specimens made from bulk adhesive at increasing cross head opening speeds are reported in this paper. The compact tension tests results showed a decreasing critical strain energy release rate with increasing cross head speed, with the critical energy release rate at 1 m/s cross head speed equal to about 20% of its quasi-static value. Two rate dependent cohesive zone models are formulated based on the compact tension test data. A cohesive de-cohesive relationship was postulated between the tractions acting across the crack faces and the opening displacement and opening velocity. These rate dependent cohesive zone models are implemented in a interface finite element to model discrete crack growth in the adhesive. The reaction force history from simulation of the DCB test is in good agreement with the test data using only the rate dependent interface element to model the adhesive.

Effect of Solvent Diffusion on Crack-Tip Fields and Driving Force for Fracture of Hydrogels

2015 ◽  
Vol 82 (8) ◽  
Author(s):  
Nikolaos Bouklas ◽  
Chad M. Landis ◽  
Rui Huang
Keyword(s):  
Boundary Conditions ◽  
Energy Release Rate ◽  
Energy Release ◽  
Crack Growth ◽  
Release Rate ◽  
Crack Tip ◽  
Far Field ◽  
Solvent Diffusion ◽  
Effect Of Solvent ◽  
Transient Energy

Hydrogels are used in a variety of applications ranging from tissue engineering to soft robotics. They often undergo large deformation coupled with solvent diffusion, and structural integrity is important when they are used as structural components. This paper presents a thermodynamically consistent method for calculating the transient energy release rate for crack growth in hydrogels based on a modified path-independent J-integral. The transient energy release rate takes into account the effect of solvent diffusion, separating the energy lost in diffusion from the energy available to drive crack growth. Numerical simulations are performed using a nonlinear transient finite element method for center-cracked hydrogel specimens, subject to remote tension under generalized plane strain conditions. The hydrogel specimen is assumed to be either immersed in a solvent or not immersed by imposing different chemical boundary conditions. Sharp crack and rounded notch models are used for small and large far-field strains, respectively. Comparisons to linear elastic fracture mechanics (LEFM) are presented for the crack-tip fields and crack opening profiles in the instantaneous and equilibrium limits. It is found that the stress singularity at the crack tip depends on both the far-field strain and the local solvent diffusion, and the latter evolves with time and depends on the chemical boundary conditions. The transient energy release rate is predicted as a function of time for the two types of boundary conditions with distinct behaviors due to solvent diffusion. Possible scenarios of delayed fracture are discussed based on evolution of the transient energy release rate.

Micromechanical Studies of Strain Rate Dependent Compressive Strength in Brittle Polycrystalline Materials

2019 ◽  
Vol 16 (04) ◽  
pp. 1844011
Author(s):  
Hao Jiang ◽  
Zongyue Fan ◽  
Jian Lu ◽  
Bo Li
Keyword(s):  
Finite Element ◽  
Energy Release Rate ◽  
Grain Boundaries ◽  
Energy Release ◽  
Release Rate ◽  
Dynamic Compression ◽  
Brittle Materials ◽  
Polycrystalline Materials ◽  
Critical Energy Release Rate ◽  
Rate Dependent

We propose a novel computational model for the high fidelity prediction of failure mechanisms in brittle polycrystalline materials. A three-dimensional finite element model of the polycrystalline structure is reconstructed to explicitly account for the micro-features such as grain sizes, grain orientations, and grain boundary misorientations. Grain boundaries are explicitly represented by a thin layer of elements with non-zero misorientation angles. In addition, the Eigen-fracture algorithm is employed to predict the crack nucleation and propagation in the grain structure. In the framework of variational fracture mechanics, an equivalent energy release rate is defined at each finite element to evaluate the local failure state by comparing to the critical energy release rate, which varies at the grain boundaries and the interior of grains. Moreover, constitutive models are considered as functions of the local microstructure features. As a result, a direct mesoscale simulation model is developed to resolve the anisotropic response, intergranular and transgranular fractures during the microstructure evolution of brittle materials under general loading conditions. A micromechanics-based interpretation for the rate dependent strength of brittle materials is derived and verified in examples of dynamic compression tests. In specific, the compressive dynamic response of hexagonal SiC with equiaxed grain structures is studied under different strain rates.

Longitudinal vertical crack analysis in beam with relaxation stresses

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Victor Rizov
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Strain Energy ◽  
Strain Energy Release Rate ◽  
Viscoelastic Model ◽  
Strain Energy Release ◽  
Time Dependent ◽  
Content Type ◽  
Dependent Strain

Purpose This paper is concerned with analysis of the time-dependent strain energy release rate for a longitudinal crack in a beam subjected to linear relaxation. A viscoelastic model with an arbitrary number of parallel units is used for treating the relaxation. Each unit has one dashpot and two springs. A stress-strain-time relationship is derived for the case when the coefficient of viscosity in each unit of the viscoelastic model changes continuously with time. The beam exhibits continuous material inhomogeneity along the thickness. Thus, the moduli of elasticity and the coefficients of viscosity vary continuously in the thickness direction. The aim of the present paper is to obtain time-dependent solutions to the strain energy release rate that take into account the relaxation when the coefficient of viscosity changes with time. Design/methodology/approach Time-dependent solutions to the strain energy release rate are derived by considering the time-dependent strain energy and also by using the compliance method. The two solutions produce identical results. Findings The variation of the strain energy release rate with time due to the relaxation is analysed. The influence of material inhomogeneity and the crack location along the beam width on the strain energy release rate are evaluated. The effects of change of the coefficients of viscosity with time and the number of units in the viscoelastic model on the strain energy release rate are assessed by applying the solutions derived. Originality/value The time-dependent strain energy release rate for a longitudinal vertical crack in a beam under relaxation is analysed for the case when the coefficients of viscosity change with time.

Influence of Creep on Longitudinal Fracture of Inhomogeneous Rod Loaded in Torsion and Bending

2021 ◽  
Vol 1046 ◽  
pp. 9-14
Author(s):  
Victor Iliev Rizov
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Strain Energy ◽  
Strain Energy Release Rate ◽  
Linear Time ◽  
Circular Cross Section ◽  
Strain Energy Release ◽  
Time Dependent ◽  
Material Inhomogeneity

The present paper analyzes the influence of creep on longitudinal fracture in continuously inhomogeneous rod of circular cross-section loaded in torsion and bending. The rod exhibits continuous material inhomogeneity in both radial and longitudinal directions. The creep is described by using non-linear time-dependent relations between the principle stresses and strains. A time-dependent solution to the strain energy release rate is derived by analyzing the complementary strain energy. The time-dependent strain energy release rate is found also by considering the energy balance for verification. The solutions are applied to perform a parametric study of the strain energy release rate under creep.

Local damage simulations of printed circuit boards based on in‐plane cohesive zone parameters

Circuit World ◽  
2013 ◽  
Vol 39 (2) ◽  
pp. 60-66 ◽  
Author(s):  
Peter Filipp Fuchs ◽  
Klaus Fellner ◽  
Gerald Pinter
Keyword(s):  
Finite Element ◽  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Cohesive Zone ◽  
Printed Circuit Boards ◽  
Circuit Board ◽  
Circuit Boards ◽  
Content Type ◽  
Printed Circuit

PurposeThe purpose of this paper is to analyse, in a finite element simulation, the failure of a multilayer printed circuit board (PCB), exposed to an impact load, to better evaluate the reliability and lifetime. Thereby the focus was set on failures in the outermost epoxy layer.Design/methodology/approachThe fracture behaviour of the affected material was characterized. The parameters of a cohesive zone law were determined by performing a double cantilever beam test and a corresponding simulation. The cohesive zone law was used in an enriched finite element local simulation model to predict the crack initiation and crack propagation. Using the determined location of the initial crack, the energy release rate at the crack tip was calculated, allowing an evaluation of the local loading situation.FindingsA good concurrence between the simulated and the experimentally observed failure pattern was observed. Calculating the energy release rate of two example PCBs, the significant influence of the chosen type on the local failure behaviour was proven.Originality/valueThe work presented in this paper allows for the simulation and evaluation of failure in the outermost epoxy layers of printed circuit boards due to impact loads.

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