Dynamic crack propagation with a variational phase-field model: limiting speed, crack branching and velocity-toughening mechanisms

We address the simulation of dynamic crack propagation in brittle materials using a regularized phase-field description, which can also be interpreted as a damage-gradient model. Benefiting from a variational framework, the dynamic evolution of the mechanical fields are obtained as a succession of energy minimizations. We investigate the capacity of such a simple model to reproduce specific experimental features of dynamic in-plane fracture. These include the crack branching phenomenon as well as the existence of a limiting crack velocity below the Rayleigh wave speed for mode I propagation. Numerical results show that, when a crack accelerates, the damaged band tends to widen in a direction perpendicular to the propagation direction, before forming two distinct macroscopic branches. This transition from a single crack propagation to a branched configuration is described by a well-defined master-curve of the apparent fracture energy $\Gamma$ as an increasing function of the crack velocity. This $\Gamma(v)$ relationship can be associated, from a macroscopic point of view, with the well-known velocity-toughening mechanism. These results also support the existence of a critical value of the energy release rate associated with branching: a critical value of approximately 2 $G_c$ is observed i.e. the fracture energy contribution of two crack tips. Finally, our work demonstrates the efficiency of the phase-field approach to simulate crack propagation dynamics interacting with heterogeneities, revealing the complex interplay between heterogeneity patterns and branching mechanisms.

Supershear bursts in the propagation of a tensile crack in linear elastic material

Fabian Barras, René Carpaij, Jean-François Molinari

Since the early years of the linear elastic theory of fracture [linear elastic fracture mechanics (LEFM)], scientists have sought to understand and predict how fast cracks grow in a material or slip fronts propagate along faults. While shear cracks can travel faster than the shear wave speed, the Rayleigh wave speed is the limiting speed theoretically predicted for tensile failure. This work uncovers the existence of supershear episodes in the tensile (mode I) rupture of linearly elastic materials beyond the maximum allowable (sub-Rayleigh) speed predicted by the classical theory of dynamic fracture. While the admissible rupture speeds predicted by LEFM are verified for smooth crack fronts, we present numerically how a supershear burst can emerge from a discontinuity in crack front curvature. Using a spectral formulation of the three-dimensional elastodynamic equations coupled with a cohesive model of fracture, we study how these short-lived bursts create shock waves persisting far from the discontinuity site. This study provides insight on crack front instabilities present in the rapid tensile failure of brittle materials due to large distortions of the rupture front.

2018

Fracture and Fatigue of Adhesively-Bonded Fiber-Reinforced Polymer Structural Joints

Ye Zhang

Being good structural replacement for other conventional material, the pultruded glass fiber reinforced polymer (GFRP) profiles are being increasingly used in civil engineering structures. The connection between components is considered the most suspect area for failure initiation. The adhesive bonding is preferred for FRP composite structures, rather than the mechanical fastening, due to the brittle failure nature of composite materials. During past decades, many efforts have been made by researchers to better understand the mechanism of adhesive bonding, to analyze the stress distributions and to improve the strength of composite structural joints. However there is still no commonly accepted design code/standard existing for adhesively-bonded joints in civil engineering infrastructures since several important knowledge gaps are to be filled. Besides the joint strength at failure, the characterization and modeling of the progressive failure process, in particular involving the so-called crack initiation and propagation phases, is also an important concern. By employing the strain energy release rate (SERR) as the fracture parameter, the linear-elastic fracture mechanics (LEFM) approach is considered an efficient method to model the fracture behavior of structural joints. However, due to the uncontrollable crack initiation and the complex geometric configurations, the crack measurement techniques and the calculation method for the SERR are to be validated. In fracture mechanics, the fracture of a material or component can be described by a single mode or the combinations of the following three basic modes: opening mode (Mode I), shearing mode (Mode II), and tearing mode (Mode III). During the fracture of a structural joint, crack initiation and propagation are driven by combined through-thickness tensile (peeling), and shear stresses, thus resulting in a mixed mode fracture. In order to use the fracture results of structural joints to form the mixed fracture criterion for a specific composite material, a feasible analytical or numerical method are to be developed to determine the Mode I and II components of the SERR during fracture. Although many efforts have been made to better understand the short-term behavior of structural joint under quasi-static loading, the long-term performance under fatigue loading and different environmental conditions is a more demanding task when adhesively-bonded joints are applied in a real structure. Most of structural failures occur due to mechanisms that are driven by fatigue loading and for composite structures, the fatigue produced by the repeated application of live load is more critical due to its lighter self-weight, in other words the lower dead load. Besides the fatigue loading, a structure in practice may also experience the combined environmental effects of two basic factors: temperature and humidity. These environmental conditions may directly affect properties of structural joints, including the failure mechanism, the stiffness and strength, the crack initiation and propagation and etc.. Thus, the missing knowledge and confidences in the long-term behavior under cyclic loading and the durability under different environmental conditions are the main obstacles to the further development of FRP composites in civil engineering infrastructures. In this research, the mechanical and fracture behavior of adhesively-bonded double-lap and stepped-lap joints (DLJs and SLJs) composed of pultruded GFRP laminates and an epoxy adhesive were experimentally and numerically investigated under both quasi-static and fatigue loadings. The crack measurement techniques and the calculation methods for the SERR were validated for DLJs and SLJs. The LEFM approach was successfully applied to characterize and model the progressive failure process of structural joints. The Mode I and II components of the SERR of DLJs and SLJs were determined using the Virtual Crack Closure Technique in finite element analysis. Combining with the results of pure Mode I and II experiments, a mixed mode fracture criterion for pultruded GFRP composite was formed. Under fatigue loading, the fatigue behavior of structural joints was successfully modeled by using the stiffness-based and fracture mechanics approaches, besides the F-N curves. Based on the stiffness degradation, a linear and a sigmoid non-linear model were established and the fatigue live corresponding to the failure and allowable stiffness degradation can be predicted. Concerning fracture mechanics approach, the Fatigue Crack Growth (FCG) curves were formed for DLJs and SLJs and the corresponding fracture parameters were obtained. Similarly to stiffness-based approach, fatigue lives corresponding to the failure and allowable crack length can be predicted. The environmental effects on both short- and long-term performances of structural joints were experimentally evaluated and numerically modeled based on experimental results. The temperature-dependent joint stiffness can be predicted using the finite element analysis based on the thermomechanical properties of constituent materials. A relationship between the equivalent quasi-static joint strength under different environmental conditions and the cyclic stresses and the fatigue life was established.

EPFL2010

Fracture and Fatigue of Adhesively-Bonded Fiber-Reinforced Polymer Structural Joints

Ye Zhang

EPFL2010