A micromechanical model is developed that generates analytic expressions for the crack displacement vector u given an arbitrary far-field stress state sigma(a) for a crack that is bridged by an array of ligaments oriented at an arbitrary angle with respect to the crack plane. The model is applicable to various materials, e.g., fibrous ceramic composites, or polymer composites reinforced by stitches or z-pins or woven tows, and deals with interfacial friction, enhanced friction due to increased contact pressure ("snubbing"), and the possibility of ligament deflection enabled by yield or damage. The model also conveniently incorporates ligament failure and rate dependent phenomena (fatigue or creep). Adaptability of the model is enabled by the definition of a standard Reference Model, which generates analytic expressions for the crack displacement for given possible yield, ligament deflection, and friction and snubbing effects and is invariant for all geometrical and material choices. The switching on or off and the strengths of all phenomena are governed by assigning values to a handful of material parameters. The material parameters will generally be calibrated against data in a top-down strategy, the model thereby mapping material selection onto engineering fracture via the predicted bridging relationship u [sigma (a) ]. The relationship u [sigma (a) ] can depend strongly on bi-angular ligament orientation. Yield and deflection can change u [sigma (a) ] qualitatively, e.g., by creating fracture surface contact even when sigma(a) includes substantial opening tension. Snubbing has significant effects, including possible stabilization of the pullout of a finite ligament. Since model output is computed via analytic expressions, its speed will support the model's use in large-scale material simulations or as constraining physical information in machine learning algorithms.

This paper presents an augmented finite element method for the fracture modeling of curved composite shell structures considering geometric nonlinear effects. We first derive the composite shell AFEM (CS-AFEM) formulation using a dynamic implicit algorithm, which enhances the numerical convergence when dealing with unstable crack propagations. Besides, the cohesive zone model featuring with shell kinematics is incorporated into the CS-AFEM to describe the quasi-brittle fracture behaviors of composite laminates. Furthermore, a coordinate transformation scheme is proposed to describe both the local material orientation and the crack evolving path in the curved shell structures. Finally, several benchmark examples are numerically investigated, and the capability of the proposed method in modeling the arbitrary evolving cracks in curved composite shell structures has been thoroughly demonstrated.

A computationally efficient fatigue analysis methodology is proposed that uses a cycle jump approach to drive the accumulation of fatigue damage and a unified local fatigue cohesive zone model that can predict the initiation and propagation of cracks using a reduced set of model parameters. A new definition of the stress ratio is proposed for general loading conditions, which include negative load ratios, unsynchronized loads, and problems where the mode mixity changes during a cycle. The cycle jump procedure was verified by performing analyses of standard double cantilever beam and mixed mode bending tests. Then, the model was validated by performing analyses of double notch shear tests and initiation of transverse matrix cracking in a [0/90] laminate using models that account for residual thermal stresses. The results indicate that the analysis methodology can reproduce experimentally measured fatigue damage initiation and evolution for a variety of different configurations and load combinations. (Keywords: C. Cohesive interface modelling, B Fatigue, B. Delamination, A. Polymer-matrix composites (PMCs))

This paper presents and validates a new local to global (L2G) FEM approach that can analyze multiple, interactive fracture processes in 2D solids with improved numerical efficiency and robustness. The method features: 1) forming local problems for individual and interactive cracks; and 2) parallel solving local problems and returning local solutions as part of the trial solution for global iteration. It has been demonstrated analytically (through a simple 1D problem) and numerically (through several benchmarking examples) that, the proposed method can substantially improve the robustness of the global solution process and significantly reduce the costly global iteration for convergence. The demonstrated improvement in numerical efficiency is up to 20∼40% for mildly unstable problems. For problems with severely unstable crack initiation and propagation, the improvement can be more significant. This new method is readily applicable to other popular methods such as the extended FEM (X-FEM), Augmented FEM (A-FEM) and Phantom-node method (PNM).

In this paper, two-dimensional (2D) orthotropic augmented finite element method (A-FEM) is applied to account for progressive failure of composite laminates under transverse loading, which considers all major cracking modes (delamination, fiber kinking/rupture matrix cracking). High-fidelity simulations of different stacking composite laminates under transverse loading are implemented. Both predicted load−deflection curves and damage evolution are in good agreement with that of experimental results, which demonstrates the numerical capability of A-FEM. In addition, the influence of stacking sequence on the failure mechanism is also studied by predicted damage evolution of laminates with different stacking sequence [Formula: see text], [Formula: see text] and [Formula: see text]. Results show that the tensile matrix crack in the bottom laminar is always the first damage mode for the composite laminate, and the subsequent crack propagation is related to ply orientation of adjacent plies which have a blocking effect on crack propagation.

This paper presents an integrated numerical algorithm based on the nonlinear augmented finite element method (N-AFEM) to accurately simulate the arbitrary evolving strong discontinuities (cracks/slip lines) and failure behaviors in geotechnical structures. A novel nonlinear elemental augmentation and condensation scheme was first proposed within the N-AFEM framework, which allows the consideration of nonlinear coupled intra-element cracks without the need of additional nodes or nodal DoFs. Then a modified exponential cohesive zone model (CZM) that considers the coupling effects between tension/compression and shear at the fracture surface was proposed to describe the fracture process of geomaterials. Besides, a nonlinear yielding function based on the Mohr-Coulomb strength theory was introduced into the framework and serves as the fracture initiation criteria for geomaterials. Finally, several benchmark examples were simulated and the predicted results were compared with existing numerical or experimental data to demonstrate the validity of the proposed method.

A nonlinear shell augmented finite element method (NS-AFEM) is proposed in this paper to account for the multiple fractures and their interactive evolutions in thin laminated composites with large deformations. This NS-AFEM employed a nonlinear elemental condensation algorithm based on Newton-Raphson method, which explicitly treated the strong discontinuity of a cracked element without the need of extra nodes. In addition, an improved geometrically nonlinear shell-like cohesive zone model (CZM) was developed and integrated into the NS-AFEM to represent the nonlinear fracture processes of composites, including matrix cracking in tension/compression, fiber tensile rupture and fiber compressive kinking, and interface delamination. The high-fidelity simulations in open-hole tension and three-point-bending tests of composite laminates demonstrate that the proposed method is capable of dealing with the geometrically nonlinear coupled crack system in thin laminated composites, which is of particular challenge in other alternative numerical methods.

A conforming augmented finite element method (C-AFEM) is extended to predict the failure process in inter-ply of fiber-reinforced composite laminates. Combining with cohesive zone model (CZM) element, the delamination between inter-plies can also be captured. Matrix fracture, fiber fracture and delamination in inter-plies will occur when the composite laminate fracture, which is a complicated process, and the current method appears capable of modelling failure mechanism of composite laminates, which is demonstrated mesh-independent, high-fidelity and robust. Different stacking open-hole composite laminates subject to tension load are tested by electrical measurement and Digital Image Correlation (DIC) system. The proposed C-AFEM is applied to model progressive failure of open-hole composite laminates and results are found to agree with experiments very well.

In this paper, an improved conforming AFEM (C-AFEM) for efficient modeling of arbitrary crack propagation and branching is proposed and validated. An explicit formulation for branching cracks has been derived within the C-AFEM framework. The conjugate gradient method is integrated into the C-AFEM formulation to solve the local problem that consists of all elements traversed by single or multiple cracks. Multiple numerical evidences show that this new approach can substantially improve the modeling efficiency. The solution accuracy and numerical robustness are also significantly improved.

This paper reports a combined numerical and experimental study on the multiple fracture evolution in carbon fiber reinforced polymer (CFRP) T-joints under pull-off load. The experimental study successfully captured the sequential fracture initiation and evolution involving a complex interplay among noodle cracking, noodle-skin and skin-stiffener delamination, and their correlation with the load-displacement curves. Numerically, two independent numerical methods, (a) the extend finite element method (X-FEM) available in ABAQUS, and (b) the augmented finite element (A-FEM) method, are used to cross-check their predictive capability in modeling progressive fracture evolution in the T-joints. It is found that, although the nonlinear load-displacement curves predicted by both methods are consistent with experimental data, their predictions on fracture progression responsible for final failure are different. The A-FEM prediction is in good agreement with experimental record while the X-FEM's prediction is inaccurate. Finally, the validated A-FEM model is coupled with the Binary Model to quantify the improvement in fracture resistance using the Z-pin reinforcement technique. The simulation results, which are validated by previously reported experimental data, show that properly arranged Z-pin reinforcement can improve the fracture tolerance and significantly delay the final failure of T-joints.

This article presents a nonlinear augmented finite element method (N‐AFEM) for the analysis of arbitrary crack initiation and propagation in large deformation plates and shells. The FE formulations for plate/shell elements and a shell‐like cohesive zone element, both with explicit consideration of geometric nonlinearity, have been derived in detail. The geometrically nonlinear shell‐like cohesive element has the essential feature of 3D but with crack displacements directly extracted from midplane shell element nodes, which enables an accurate description of crack propagation in shells and plates under large deformation. Furthermore, a novel augmentation process that can explicitly account for the discontinuous displacement fields of cracked elements without the need of extra nodes or nodal DoFs has been develop based on a nonlinear Newton‐Raphson method. The numerical performance of the N‐AFEM in modeling a number of benchmark shell/plate fracture problems demonstrates that the method is efficient, accurate, and robust.

Aligned short carbon fiber (3-5 mm) thermoplastic composites have potential for versatile manufacturability with little loss of mechanical properties in comparison to continuous reinforcement. Property prediction, failure behavior, and the effects of microstructural variation for these materials are not yet well explored. The finite element method was used to evaluate large domains encompassing characteristic discontinuous microstructures of thermoplastic matrix (PMMA) composites reinforced with short 3 to 5 mm carbon fibers with a high degree of alignment and conventional volume fractions. Virtual tests were performed on highly detailed microstructural simulations which included fiber-matrix interface representation along with uniform or misaligned fiber morphologies. Stiffness, strength, and failure mechanisms were analyzed. It was shown that for ideal uniformly aligned short fiber reinforcements, the material maintains a high modulus within 95% of an equivalent continuous fiber-reinforced polymer, along with relatively high strength at 80% of a carbon fiber reinforced polymer (CFRP). Failure modes depended on the toughness of the fiber-matrix interface, transitioning from fiber rupture to a weaker fiber pullout failure for low interface properties. Simulations indicated that significant fiber misalignments on the order of 15% of fibers at +/- 15 degrees off-axis could sharply reduce local strength in the misaligned region to roughly 20% of the continuous fiber strength. Although partially affected by property dropoff owing to fiber off-axis misalignment, this weakening was largely due to local matrix pockets in regions of high misalignment, which acted as failure initiation points.

This paper, for the first time in literature, formulated and validated a three-dimensional, nonlinear augmented finite element method (3D A-FEM) that can account for multiple crack evolution in laminated composites under large deformation. The 3D A-FEM accounts for all major cracking events (intra-ply matrix cracking, fiber rupture/kinking, and inter-ply delamination) with explicit cohesive cracks. The computational scheme is achieved by coupling the 3D A-FEs for intra-ply cracks with 3D cohesive interface elements for inter-ply delamination. The strong discontinuities of both intra- and inter-ply cracks are explicitly represented by the geometrically nonlinear cohesive zone models (CZMs). The numerical capability is demonstrated by several benchmark tests with both in-plane and out-of-plane loadings. Results show that the A-FEM predicted progressive damage processes, including the arbitrary initiation of multiple cracks and their nonlinearly coupled progression with delamination all the way up to the final catastrophic failure, are all in good agreement with experimental results. (C) 2020 Elsevier Ltd. All rights reserved.

This paper presents a conforming augmented finite element method (C-AFEM) that can account for arbitrary cracking in solids with similar accuracy of other conforming methods, but with a significantly improved numerical efficiency of about ten times. We show that the numerical gains are mainly due to our proposed new solving procedure, which involves solving a local problem for crack propagation and a global problem for structural equilibrium, through a tightly coupled two-step process. Through several numerical benchmarking examples, we further demonstrate that the C-AFEM is more accurate and mesh insensitive when compared with the original A-FEM, and both C-AFEM and A-FEM are much more robust and efficient than other parallel methods including the extended finite element method (XFEM)/generalized finite element (GFEM) and the conforming embedded discontinuity method.

The use of externally-bonded composite materials for strengthening and rehabilitation of existing structures is among the most popular reinforcement techniques. Technologies, such as Fabric Reinforced Cementitious Matrix (FRCM) have been recently developed to address some of the issues of Fiber Reinforced Polymers (FRP), such as sensitivity to elevated temperatures and UV, impermeability, restricted application in presence of moisture or uneven substrate. For a detailed strengthening design with FRCM composites, the mechanical properties of the materials are required. Analytical models in literature discuss the interaction between the FRCM matrix and fabric using a fracture mechanics approach. These analytical laws were simplified using a trilinear curve in which a constant branch correlated to the friction is added. In the United States, “Acceptance Criteria AC434” includes the test methods to evaluate the mechanical properties of the FRCM through a direct tensile test which uses clevis grips. The material characterization per AC434 is in harmony with ACI 549.4R design guidelines. This study deals with the analysis of FRCM materials using 2D Augmented-Finite Element Method (A-FEM) approach. Constitutive material behaviors were used to implement on A-FE model, which can predict the failure modes of the composite material. The damage of the mortar was described by a trilinear curve, and the number and position of the cracks were fixed preliminarily. The fabric was modelled as a continuum layer attached to the mortar with no-thickness cohesive elements. The cohesive law between fabric and mortar was taken from the literature. The tensile test on the FRCM coupon with one layer of fabric was numerically modeled and compared to the experimental stress-strain curves. Results show that the numerical curves matched the experimental ones and capture the three branches of the FRCM constitutive law as well as the failure mode. This modelling tool will allow researchers to predict the constitutive law of an FRCM mater

In this paper, we extended a recently developed augmented finite element method (A-FEM) to account for the complicated progressive damage processes in laminated composites, which are of orthotropic nature and typically develop multiple types of cracking systems including intra-ply matrix/fiber splitting, fiber rupture in tension and/or kinking in compression, and inter-ply delamination. The orthotropic A-FEM represents all of these major damage modes with improved nonlinear cohesive zone models (CZMs) that explicitly consider the asymmetric tension- and compression-responses. A rigorous verification and validation process demonstrates that the developed orthotropic A-FEM can adequately account for the initiation and propagation of various types of cracks and their coupled evolution under complex stress environments. A-FEM predictions to progressive damage processes in several multidirectional notched and un-notched laminates, including the initiation of multiple cracks and their nonlinearly coupled progression with delaminations all the way up to the final, catastrophic failure, are all in excellent agreement with experimental measurements and observations.

This paper presents an efficient multiscale approach for high fidelity virtual testing of highly aligned short fiber reinforced composites (SFRCs), based solely on constituent material and interface properties with no need of calibration data. The method is based on a hierarchical, bottom-up characterization of SFRCs and the link of mechanical behaviors of materials and microstructures from a lower scale to a higher scale. It starts with a microscopic unit cell model to estimate the transverse and shear properties of the aligned short fiber composites. Next, two types of mesoscale models with explicit consideration of fiber discontinuity and possible local fiber misalignments are employed to obtain effective properties of material domains with such morphologies. Such obtained meso-scale mechanical properties and damage behaviors are then integrated into the macroscale virtual laminar via the stochastically integrating of possible material defects. Results indicate that for perfectly aligned SFRCs the strength reduction is about 25% as compared to that of the continuously reinforced composites. However, misalignment of short fibers can cause a further strength reduction of 20–35% with the volume fraction of the misalign regions varying from 1% to 10%.

This paper reports an experimental study on mechanical response of single-lap bolted composite interference-fit joints in their entire life span. Particular focus was given to interface behavior, bearing response, strain distribution and out-of-plane deformation under varying multiple parameters including interference-fit percentage, tightening torque and stacking sequence. The 3D digital image correlation system was used to characterize development of strain concentration and deformation. Microscopy studies on coupled interface and bearing plane were conducted to understand the damage mechanism. It‘s found that the bolt-inserting can act as cold expansion which facilitates forming tightly coupled interface and prohibits inclination of bolt. The linear phase of stress-strain behavior is prolonged by tightening torque which inhibits delamination growth in bearing plane, induces friction force to balance external load and postpones bolt-to-hole bearing action. The strain around the hole goes through a switch from release of residual pressure on tensile side to squeezing on bearing side. During the switch the interface keeps tightly coupled without delay in load take-up. Strain concentration bands were observed in the joints with highly anisotropic laminates, whereas it is localized around bolt-hole in quasi-isotropic laminates. The joint structure possesses its own response characteristics which are beyond extrapolation from ply properties.

In the current study a high fidelity analysis approach is used to predict the failure process of notched composite structures. Discrete cracking is explicitly modelled by incorporating cohesive interface elements along potential failure paths. These elements form an interconnected network to account for the interaction between interlaminar and intralaminar failure modes. Finite element models of these configurations were created in the commercial analysis software ABAQUS and a user defined material subroutine (UMAT) was used to describe the behaviour of the cohesive elements. The material subroutine ensured that the model remained stable despite significant damage, which is a significant challenge for implicit damage simulations. Two analysis approaches were adopted using either the as-measured or modified (in-situ) ply strengths. Both approaches were capable of closely predicting the mean ultimate strength for a range of hole diameters. However, using the measured ply properties resulted in extensive matrix cracking in the surface ply which caused a deviation from the experimentally measured surface strain. The results demonstrate that high fidelity physically based modelling approaches have the ability to complement or replace certain experimental programs focussed on the design and certification of composite structures.

This paper describes an experimental study on the fretting behaviors and tribological mechanism of interface between carbon fiber reinforced polymer (CFRP) composites and titanium alloy in composite interference-fit joints under service condition. A ball-on-flat configuration was employed in the fretting tests where the effect of fiber orientation, ambient temperature, surface treatment and interface condition were evaluated. The coefficients of friction (COFs), 3D surface morphologies and microstructures of worn scars were presented to characterize corresponding fretting mechanisms. An obvious tribological anisotropy was observed in the CFRP specimens where the longitudinal surface possessed much smaller COFs and less wear damage than the normal surface. The wear damage and anisotropic properties can be reduced to a certain extent by surface treatment through improving wear resistance or serving as solid lubricant respectively. The fretting behaviors also show strong temperature dependence. The increasing temperature exaggerates deformation in longitudinal surface and aggravates abrasion in normal surface by softening matrix resin. Wet service condition contributes to reducing COF and wear owing to the formation of a tribofilm on the interface.