Time-dependent Damage Evolution Research Articles

A novel time-dependent damage constitutive model for hard rock materials

The mechanical behavior of deep hard rocks plays a crucial role in the long-term safety and stability of engineering structures. This work focuses on studying the instantaneous and time-dependent fracture propagation of hard rock materials from a theoretical perspective. A new unified constitutive model, based on a modified Mohr–Coulomb (M-C) criterion, is proposed to accurately represent the short and long-term mechanical properties of hard rocks. To capture the strain hardening and strain softening behaviors, damage is utilized as an internal mechanism-driven variable, controlling the expansion and contraction of the plastic yield surface. Additionally, a combination of time-dependent damage law and viscoplastic theory is employed to account for nonlinear creep deformation characteristics. By considering the time-dependent effects, the model can be applied to both instantaneous loading and creep conditions. The general algorithm format is derived in detail, and an explicit integration algorithm is utilized to update the time-dependent damage evolution. Finally, the proposed model is validated by comparing its predictions with the short and long-term mechanical responses of Beishan granite and Rumei dacite. This comprehensive constitutive model improves our understanding of continuum damage mechanics and provides a scientific basis for analyzing and evaluating the long-term safety and stability of deep hard rock engineering projects.

Time-dependent creep fatigue damage evolution in C/SiC composite: Theory and analytical prediction

In this paper, the time-dependent damage evolution in carbon fiber-reinforced silicon carbide ceramic-matrix composites (C/SiC CMCs) under creep fatigue loading at elevated temperature was analyzed using a micromechanical approach. Synergistic effects of creep fatigue peak stress level and damage in the matrix and the interface on time-dependent damage evolution in C/SiC composites were analyzed. Next, relationships of time-dependent creep fatigue damage mechanisms, damage parameters, environmental temperature and duration were determined. Then, the effects of composite constituent properties, creep fatigue damage state, environmental temperature, and duration on time-dependent damage evolution in C/SiC composites were analyzed. Furthermore, time-dependent composite strain response and interface debonding and oxidation state in C/SiC composite under different creep fatigue peak stress levels were predicted. Under creep fatigue loading, the composite internal damage evolution contributed to the increased time/temperature-dependent composite peak strain. Hysteresis-based damage parameters were developed and utilized to monitor C/SiC composite internal damage evolution. Under creep fatigue loading, the hysteresis area and width increased with oxidation duration to a peak value and remained constant, and the hysteresis modulus decreased with oxidation duration.

A two-scale hydro-mechanical-damage model for simulation of preferential gas flow in saturated clayey host rocks for nuclear repository

Significant amounts of gases could be generated in the post-phase of radioactive waste repositories, which may deteriorate the integrity of natural host rocks. A safety issue related to the geological disposal facilities concerns the gas migration through saturated host rocks, of which the dominant process is mainly referred to the advective gas flow, accompanied by the formation of micro-fracturing that occurs at the applied gas pressure significantly lower than the minimum principal stress (compressive stress is regarded to be positive here). These fracture formed gas pathways are found to be highly localized and dynamically unstable, which may vary temporally and spatially within the clayey rocks. A multiscale model incorporating the evolving microcracks may be appropriate to address this specific rupture pattern. The model is developed from the periodically distributed microstructures with microcracks in a porous medium. The upscaling method based on the asymptotic expansions leads to the macroscopic hydro-mechanical (HM) governing equations coupled with the normalized microcrack length. Based on the micro-mechanical energy analysis, the time-dependent damage evolution law is constructed that accounts for the subcritical microcrack propagation. The local macroscopic response of the model is analyzed with emphasis on the influence of the microstructural size, the loading rate and the reference crack velocity, which are important factors influencing the localized pathways for gas migration. Two numerical examples of air injection tests on clayey rocks are presented where the highly localized gas pathways are explicitly simulated. The comparison between the model predictions and the experimental results provides in-depth understanding of gas induced fracturing process.

A two-scale time dependent damage model for preferential gas flow in clayey rock materials

Understanding of the gas migration within the host rock is critical for the safety assessment of a deep geological repository for radioactive wastes. However, localized gas flow in clayey host rock materials is a complex behavior associated with dynamic and unstable network of dilatant pathways, which are accompanied by micro-cracking that indicates macroscopic tensile fractures. The subcritical crack propagation at the microscale may represent the mechanism of time dependent damage observed at the macroscale. A two-scale damage model is developed in this study to explicitly simulate the preferential gas flow in clayey rock materials. A homogenization method based on asymptotic developments is employed to deduce the macroscopic damage behavior coupled with the poroelastic system, which initiates from the periodically distributed microstructures with micro-cracks. A time dependent damage evolution law is constructed based on the microscopic phenomena and the corresponding intrinsic permeability model is proposed which implicitly accounts for the fracture opening induced permeability change. The local macroscopic response of the model is analyzed and validated against the experimentally measured direct tensile strength, which illustrates the homogenized elastic and permeability coefficients, and highlights the influence of several parameters, i.e., the initial damage, the microstructural size and the strain rate. Numerical examples are presented in order to illustrate the global macroscopic response, in which a pure mechanical test, i.e., uniaxial tension test is simulated and verified against the laboratory results, then the simulation of preferential gas flow is illustrated together with the comparison of experimental explanation. The numerical results showed that the proposed two-scale model can explicitly simulate the gas induced fracturing, in which the damage propagation and the dilatant gas pathways are well captured.

Time-dependent damage analysis for viscoelastic-viscoplastic structural laminates under biaxial loading

Many composite structures are required to sustain severe thermo-mechanical loads over extended periods of time, during which viscoelastic and viscoplastic behavior can cause the progression of micro-damage. In this paper, a new computational multi-scale model that couples micro-damage mechanics with Schapery’s theory of viscoelasticity and viscoplasticity has been developed to predict time-dependent damage evolution in laminates under constant biaxial loading. After validation with experimental data, the new model capabilities are showcased by predicting damage evolution in two distinct laminates under different axial and transverse loads over time. It is found that damage evolution in both laminates is highly sensitive to the biaxial loading levels, and that crack multiplication in each ply is dependent on stacking sequence and ply orientation. The developed multi-scale model may be a suitable design tool for composite structures required to endure long-term loads in demanding environments.

Development of a synergistic damage mechanics model to predict evolution of ply cracking and stiffness changes in multidirectional composite laminates under creep

A physics-based multi-scale model that couples viscoelasticity and time-dependent damage evolution for general multidirectional laminates subjected to long-term creep loading is developed. The viscoelastic ply behavior is evaluated using a nonlinear Schapery-type viscoelastic model, while a methodology employed within the framework of classical laminate theory is used to predict the corresponding laminate time-dependent response. The evolution of microscopic ply cracks in multiple plies with different orientations during creep loading is predicted using an energy-based approach, and the corresponding laminate stiffness degradation is evaluated using a synergistic damage mechanics-based model that relies on computational micromechanics in lieu of costly experimental data. The developed model is used to predict the evolution of ply cracks and the viscoelastic stress–strain response of various cross-ply and multidirectional laminates under quasi-static and creep loading. Predicted strains, compliance changes and crack density evolutions show excellent agreement with available experimental creep data for different laminate stacking sequences, providing validation for the model. Predictions are also made for two additional multidirectional laminates in order to investigate the effect of off-axis ply angle on the creep response, which demonstrates the versatility of the model and its usefulness in assessing the long-term durability of general multidirectional composite laminates.

Model for prediction of simultaneous time-dependent damage evolution in multiple plies of multidirectional polymer composite laminates and its influence on creep

A model to predict time-dependent evolution of simultaneous transverse cracking developed in multiple plies during creep loading and its effects on creep of multidirectional polymer matrix composite laminates is presented. The stress states in the intact regions of the plies are determined using the lamination theory during an incremental change in time. The stored elastic energy, determined using this stress state, is compared with a critical stored elastic energy value for damage to determine if a ply would fracture after the increment. If fracture is predicted, variational analysis is used to determine the perturbation in ply stresses due to cracking. This procedure is repeated to determine the crack evolution and creep strain. Model predictions compared well with experimental results for a [±θm/90n]s laminate.

Long-term Corrosion Studies of a CFRP/EN AW-6060-T6 Self-piercing rivet Joint and a Steel/EN AW-6060-T6 Blind Rivet Joint

The corrosion behaviour of the aluminium alloy EN AW-6060-T6 in a self-piercing rivet joint and in a blind rivet joint was investigated by the VDA 621-415 climate chamber test for multiple corrosion cycles. After each cycle the aluminium alloy was analysed in the most damaged region that was found close to the overlap of the joints. The time-dependent damage evolution was evaluated by interferometry involving a subsequent pit volume calculation. Moreover, the potentiodynamic polarisation behaviour of each joint component was analysed in the 5wt.% sodium chloride solution which is used in the salt spray test during the test according to VDA 621-415. By graphic explorations of the polarisation curves, the galvanic corrosion characteristics were examined and the pitting corrosion susceptibility of the aluminium alloy in the joints was evaluated. It was found, that the results of the graphically data extraction correlate to the corrosion behaviour during the long-term exposure test for both joints. Moreover, the pit volume - cycle number relation exhibited a stepwise damage behaviour of the aluminium alloy in the blind rivet joint. After the end of the climate chamber tests the aluminium alloy in the blind rivet joint revealed stronger corrosion damage in less exposure time than in the self-piercing rivet joint.

One-dimensional approach to modeling damage evolution in galvanic corrosion

A one-dimensional mathematical model is developed to describe time-dependent damage evolution in well-mixed (spatially uniform species concentrations) galvanic systems using an IR drop approach. An asymptotic procedure taking advantage of disparity in length scales (thin film approximation for the electrolyte thickness) is used to derive the model. Limitations that result from the reduction of dimension are described, along with an analysis demonstrating the ability of the 1D model to capture physical phenomena, such as area ratio effects. Computed potential, current density, and corrosion damage profiles are compared and verified with experimental data available in the literature and 2D galvanic corrosion simulations. Fully derived governing equations for several different 1D geometries are presented.

Damage growth modeling using the Thick Level Set (TLS) approach: Efficient discretization for quasi-static loadings

The Thick Level Set (TLS) model is a damage model containing a non-local treatment that prevents from spurious localization issues. It also offers an automatic transition from damage to fracture. The TLS approach to model damage growth was first presented in Möes et al. [24] with a first numerical implementation for a time-dependent damage evolution law. In this paper, we propose some improvements in terms of discretization and explicit damage growth algorithms to obtain a robust, efficient and easy-to-implement model. These improvements include a simple and efficient variational formulation for computing the non-local quantities as well as the introduction of a so-called ramped Heaviside enrichment function to properly take into account the transition to cracks in fully damaged zones. We consider here a simple explicit formulation for quasi-static loadings, decoupling the elastic computation and the damage growth. The method is validated through standard benchmarks and compared to the Griffith’s fracture theory. The convergence of energy and displacement errors is observed. More complex computations including damage initiations are eventually performed.

Time-dependent damage evolution and failure in materials.mII.mSimulations

A two-dimensional triangular spring network model is used to investigate the time-dependent damage evolution and failure of model materials in which the damage formation is a nucleated event. The probability of damage formation r(i)(t) at site i at time t is taken to be proportional to the local stress at site i raised to a power: r(i)(t) = A sigma(i)(t)(eta). As damage evolves in the material, the stress state becomes heterogeneous and drives preferential damage evolution in regions of high stress. As predicted by an analytical model and observed in previous electrical fuse network simulations, there is a transition in the failure behavior at eta = 2: for eta less than or equal to 2, the failure time and damage density are independent of the system size; for eta textgreater 2, the failure time and damage decrease with increasing time and failure occurs by the formation of a finite Critical damage region which rapidly propagates across the remainder of the material. The stress distribution prior to failure exhibits no abrupt changes or scalings that indicate imminent failure. The scalings of the failure time and the failure time distribution are investigated, and compared with analytic predictions. The failure time scales as a power law in In N-T, where N-T is the system size, but the exponent is not the predicted value of 1 - eta/2; this is attributed to a difference in the stress concentration factors (scf) between the discrete lattice and a continuum model. Using the scf values for the lattice lead to predicted scalings consistent with the simulations. Predicted absolute failure times versus size are generally in good agreement with simulation results at larger eta values. The coefficient of variation of the failure time distribution is observed to be nearly constant, in slight contrast to the predicted scaling of (InNT)(-1). Overall, the simulation results quantitatively and qualitatively validate many of the critical predictions of the analytic model.

Time-dependent failure in fiber-reinforced composites by fiber degradation

The failure of fiber-reinforced ceramic and metal matrix composites under a fixed load for extended times occurs because of strength degradation in the constituent fibers. Specifically, the ceramic fibers possess a Weibull strength distribution caused by crack-like flaws, which can grow according to a power-law growth mechanism. Failure of individual fibers causes interfacial slippage and stress redistribution to unfailed fibers, which in turn accelerates the degradation rate of the remaining fibers, and culminates in abrupt failure of the composite after sufficient damage has accumulated. This sequence of events is modeled both analytically and numerically within the Global Load Sharing (GLS) approximation previously utilized for quasi-static loading. Analytically, a general constitutive model for the relationship between the stress on the damaged fiber bundle, the strain in the unbroken fibers, and the extent of damage, is combined with a time-dependent damage evolution equation derived from the slow-crack-growth kinetics to yield an integral equation for the strain vs time at fixed applied load. The relevant gauge length for a fixed-load rupture process is found to be δ = rσ τ which is twice the slip length prevailing at the initial applied load σ, where τ is the interfacial sliding resistance between fiber and matrix. The underlying time scale for rupture is the time scale for a typical fiber of gauge length δ to fail under the applied load σ; this time can be quite different from that measured by stress-rupture tests on single fibers at an unrelated laboratory gauge length L 0. A simple, accurate but approximate relationship between applied load, time to failure, fiber Weibull modulus, and slow crack growth exponent is presented. The numerical simulations of the same degradation process verify the general accuracy of the failure time obtained from the analytic results. The remaining tensile strength after some time at load but prior to failure is also studied, and the simulation results generally exhibited a more sudden-death failure than the analytical predictions. A specific application to the failure of a Nicalon fiber composite is presented.

Time-dependent damage in carbon fibre-reinforced polymer composites

Time-dependent damage (matrix cracks) evolution in AS4/3501-6 cross-ply laminates was studied using constant strain rate and constant stress tests. First ply failure stress and strain as well as the matrix crack density at a given stress level were found to be strongly dependent on strain rate. Matrix crack density increased with creep time at a constant stress level. The compliance and creep rate of the laminate increased in the presence of these cracks. These results emphasize the importance of the knowledge of time-dependent damage evolution in a lamina/laminate of a polymer composite for reliable prediction of creep and creep rupture.