Fracture characterization of bonded composites: A comparative study

Bonded joints have important benefits over conventional joining techniques such as rivets, welding, bolts and nuts in structural applications, particularly for components prepared of composite or polymeric materials. Due to the involvement of many geometric, material and construction variables, and the complex fracture and mechanical modes offered in the bonded joints, a proper consideration of fracture behavior is required to fully achieve their benefits. The fractures in bonded joints are mainly of three types; interlaminar (delamination), adhesive (interfacial) and cohesive crack. For a particular defect, crack propagation may occur in the tensile (mode I), the shear (mode II), and the tear (mode III) and their combinations (mixed mode). This study deals with topics such as theories of bonded composite joints and repairs, finite element analysis and fracture-based analysis and tests of mixed-mode cohesive, interfacial and interlaminar fracture mechanics. By employing geometrical factors extracted from finite element analysis and experimental results obtained from a modified Arcan test fixture, the mixed-mode cohesive, interfacial, and interlaminar fracture toughness are determined and fracture surfaces obtained are discussed.

Numerical Simulation of the Fracture Behavior of High-Performance Fiber-Reinforced Concrete by Using a Cohesive Crack-Based Inverse Analysis

Fiber-reinforced concrete (FRC) has become an alternative for structural applications due its outstanding mechanical properties. The appearance of new types of fibres and the fibre cocktails that can be configured by mixing them has created FRC that clearly exceeds the minimum mechanical properties required in the standards. Consequently, in order to take full advantage of the contribution of the fibres in construction projects, it is of interest to have constitutive models that simulate the behaviour of the materials. This study aimed to simulate the fracture behaviour of five types of FRC, three with steel fibres, one with a combination of two types of steel fibers, and one with a combination of polyolefin fibres and two types of steel fibres, by means of an inverse analysis based on the cohesive crack approach. The results of the numerical simulations defined the softening functions of each FRC formulation and have pointed out the synergies that are created through use of fibre cocktails. The information supplied can be of help to engineers in designing structures with high-performance FRC.

The Impacts of Increased Ductility in Organic-Rich Shale on Fracture Network Growth by Hydraulic Fracturing

The difficulty of hydraulic fracturing in organic-rich shale caused by the increased ductility has not been well interpreted quantitatively, although it is well perceived that the increased shale ductility can impede the propagation of hydraulic fractures and enhance the healing of created fractures upon injection shutdown. This study aims to quantitatively study the impacts of increased ductility on the stimulated reservoir volume (SRV) using an advanced XFEM-based simulator. To achieve this goal, a modified cohesive zone model has been integrated into an in-house fully coupled poroelastic XFEM framework. The study continues by extending the functionality of the numerical framework to simulating multiple interacting fractures. The utilization of the object-oriented programming paradigm in the development of the framework makes it an easy extension to include the multi-fracture network by creating more instances of crack segments. A main hydraulic fracture with an arbitrary number of intersected branches can thus be modeled. A series of parametric studies will be conducted to investigate the impacts of increased ductility on the induced SRV by varying four involved material parameters individually. The modified cohesive zone model, which is essentially a traction-separation law (TSL), is characterized by four parameters: the initial tensile strength Tini, ultimate tensile strength Tkrg, the critical separation Dc, and the final crack separation Dmax. It can flexibly model different crack opening scenarios and simulate more realistically the increased shale ductility. The fully coupled poroelastic XFEM framework has been comprehensively verified against the latest semi-analytical solutions on the four well-known propagation regimes. The numerical results show that the shape of TSL does affect the main hydraulic fracture growth as well as the evolvement of the fracture network, given the same cohesive crack energy and tensile strength. It infers that ductility is not only controlled by cohesive crack energy and tensile strength, which further indicates the necessity of the newly proposed cohesive zone model. The magnitude of the initial tensile strength, controlling when the cohesive crack starts propagating, is found to have the greatest impacts on the fracture length, and SRV, among all four TSL parameters. The novelty of this study is two-fold. First, the newly modified cohesive zone model can more realistically represent the increased shale ductility. Second, the advanced XFEM framework that enables the simulation of a fracture network can study the impacts of increased ductility on the whole SRV but not a single crack.

Investigations on the Directional Propagation of Hydraulic Fracture in Hard Roof of Mine: Utilizing a Set of Fractures and the Stress Disturbance of Hydraulic Fracture

Directional fracturing is fundamental to weakening the hard roof in the mine. However, due to the significant stress disturbance in the mine, principal stresses present complicated and unmeasurable. Consequently, the designed hydraulic fracture (HF) extension path is always oblique to principal stresses. Then, the HF will present deflecting propagation, which will restrict the weakness of the hard roof. In this work, we proposed an approach to drive the HF to propagate directionally in the hard roof, utilizing a set of hydraulic fractures and their stress disturbance. In this approach, directional fracturing in the hard roof is conducted via the sequential fracturing of three linear distribution slots. The disturbed stresses produced by the first fracturing (in the middle) are utilized to restrict the HF deflecting extension of the subsequent fracturing. Then, the combined hydraulic fractures constitute a roughly directional fracturing trajectory in rock, i.e., the directional fracturing. To validate the directional fracturing approach, the cohesive crack (representing rock fracture process zone (FPZ)) model coupled with the extended finite element method (XFEM) was employed to simulate the 2D hydraulic fracturing process. The benchmark of the above fracturing simulation method was firstly conducted, which presents the high consistency between simulation results and the fracturing experiments. Then, the published geological data of the hard roof in Datong coal mine (in Shanxi, China) was employed in the fracturing simulation model, with various principal stress differences (2~6 MPa) and designed fracturing directions (30°~60°). The simulation results show that the disturbing stress of the first fracturing significantly inhibits the deflecting propagation of the subsequent fractures. More specifically, along the direction parallel to the initial minimum principal stress, the extension distance of the subsequent hydraulic fractures is 2~3 times higher than that of the deflecting HF in the first fracturing. The fracturing trajectory of the proposed direction fracturing method deviates from the designed fracturing path by only 2°~14°, reduced by 76%~93% compared with the traditional fracturing method utilizing a single hydraulic fracture. This newly proposed method can enhance the HF directional propagation ability more effectively and conveniently in the complex and unmeasurable stress field. Besides, this directional fracturing method can also provide references for the directional fracturing in the oil-gas and geothermal reservoir.

Numerical Simulation of the Fracture Behaviour of High-Performance Fibre Reinforced Concrete by Using a Cohesive-Crack-Based Inverse Analysis

Fibre reinforced concrete (FRC) has become an alternative for structural applications due its outstanding mechanical properties. The appearance of new types of fibres and the fibre cocktails that can be configured mixing them has created FRC that clearly exceed the minimum mechanical properties required in the standards. Consequently, in order to take full advantage of the contribution of the fibres in construction projects, it is of great interest to have constitutive models that simulate the behaviour of the materials. This study aimed to simulate the fracture behaviour of five types of FRC, three with steel hooked fibres, one with a combination of two types of steel fibres and one with a combination of polyolefin fibres and two types of steel fibres, by means of an inverse analysis based on the cohesive crack approach. The results of the numerical simulations defined the softening functions of each FRC formulation and have pointed out the synergies that are created through use of fibre cocktails. The information obtained might suppose a remarkable advance for designers using high-performance FRC in structural elements.

Scale Bridging in Computational Modelling of Quasi-Brittle Fracture of Cementitious Composites

Computational prediction damage in cementitious composites, as steel fibre reinforced ones, under mechanical, thermal, etc. loads, manifested as creation of micro-fractured zones, followed by potential initiation and evolution of macroscopic cracks, is a rather delicate matter, due to the necessity of bridging between micro-and macro-scales. This short paper presents a relatively simple approach, based on the nonlocal viscoelasticity model, coupled with cohesive crack analysis, using extended finite element techniques. Such model admits proper verification of its existence and convergence results, from the physical and mathematical formulation up to software implementation of relevant algorithms. Its practical applicability is documented on a sequence of representative computational examples.

SEMINAL DEVELOPMENTS IN THE DURABILITY AND DAMAGE TOLERANCE ASSESSMENT OF BONDED JOINTS

Structural adhesives are widely used for joining composite components in many industries and crack growth in such materials is far more likely to occur when they are subjected to repeated cyclic loading than to monotonic loading. Whilst the Hartman- Schijve equation for fatigue crack growth (FCG) has been shown to hold for cohesive crack growth in adhesives under Mode I, Mode II and Mixed-Mode I/II loading, little attention has been paid to its ability to capture the effects of the thickness of the adhesive layer. The present paper examines the growth of fatigue cracks, that occurs cohesively through the adhesive layer, in two toughened epoxy adhesives typical of those used in the automotive and the aerospace industries. Firstly, it is established that when the crack growth rate, da/dN, curves are expressed as a function of Δ√G, or ΔG, where G is the energy release-rate, then the crack growth curves are a function of the thickness of the adhesive layer. It is then shown that this dependency vanishes when da/dN is expressed as a function of the crack-driving force, Δκ, as defined by the Hartman-Schijve equation. Therefore, it is suggested that the parameter Δκ appears to be a valid similitude parameter.

Numerical integration in G/XFEM analysis of 2-D fracture mechanics problems for physically nonlinear material and cohesive crack propagation

PurposeThe aim of this paper is to present a novel data transfer technique to simulate, by G/XFEM, a cohesive crack propagation coupled with a smeared damage model. The efficiency of this technique is evaluated in terms of processing time, number of Newton–Raphson iterations and accuracy of structural response.Design/methodology/approachThe cohesive crack is represented by the G/XFEM enrichment strategy. The elements crossed by the crack are divided into triangular cells. The smeared crack model is used to describe the material behavior. In the nonlinear solution of the problem, state variables associated with the original numerical integration points need to be transferred to new points created with the triangular subdivision. A nonlocal strategy is tailored to transfer the scalar and tensor variables of the constitutive model. The performance of this technique is numerically evaluated.FindingsWhen compared with standard Gauss quadrature integration scheme, the proposed strategy may deliver a slightly superior computational efficiency in terms of processing time. The weighting function parameter used in the nonlocal transfer strategy plays an important role. The equilibrium state in the interactive-incremental solution process is not severely penalized and is readily recovered. The advantages of such proposed technique tend to be even more pronounced in more complex and finer meshes.Originality/valueThis work presents a novel data transfer technique based on the ideas of the nonlocal formulation of the state variables and specially tailored to the simulation of cohesive crack propagation in materials governed by the smeared crack constitutive model.

Modelling Rock Fracture Induced By Hydraulic Pulses

Soft cyclic hydraulic fracturing has become an effective technology used in subsurface energy extraction which utilises cyclic hydraulic flow pressure to fracture rock. This new technique induces fatigue of rock to reduce the breakdown pressure and potentially the associated risk of seismicity. To control the fracturing process and achieve desirable fracture networks for enhanced permeability, the rock response under cyclic hydraulic stimulation needs to be understood. However, the mechanism for cyclic stimulation-induced fatigue of rock is rather unclear and to date there is no implementation of fatigue degradation in modelling the rock response under hydraulic cyclic loading. This makes accurate prediction of rock fracture under cyclic hydraulic pressure impossible. This paper develops a numerical method to model rock fracture induced by hydraulic pulses with consideration of rock fatigue. The fatigue degradation is based on S–N curves (S for cyclic stress and N for cycles to failure) and implemented into the constitutive relationship for fracture of rock using in-house FORTRAN scripts and ABAQUS solver. The cohesive crack model is used to simulate discrete crack propagation in the rock which is coupled with hydraulic flow and pore pressure capability. The developed numerical model is validated via experimental results of pulsating hydraulic fracturing of the rock. The effects of flow rate and frequency of cyclic injection on borehole pressure development are investigated. A new loading strategy for pulsating hydraulic fracturing is proposed. It has been found that hydraulic pulses can reduce the breakdown pressure of rock by 10–18% upon 10–4000 cycles. Using the new loading strategy, a slow and steady rock fracture process is obtained while the failure pressure is reduced.