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This paper describes progress on the development of theoretical models required for studying failure mechanism, crack initiation and growth around the boreholes driven by hydrofracturing processes in Hot Dry Rock (HDR) reservoirs of geothermal energy. Due to the importance of the stress intensity factor concept (K) in Fracture Mechanics, some advanced modeling techniques for accurate and fast determination of K for relevant problems are proposed. Alternative tools to deal with stress intensity factor determination are developed and assessed from the points of view of accuracy and computational cost. We concentrate on residual strength, crack initiation and crack growth as a means to model and understand experimentally observed behaviors. Several modeling methods such as compounding and weight function techniques, and boundary and finite element modeling for stress intensity factor calculation are discussed. Further to reviews of those techniques, work performed included (i) developing alternative solutions to deal with boundary‐to‐boundary interaction when using the compounding technique, (ii) relating the precision of K calculations with the level of precision of the crack opening displacement of a reference solution, in order to assess the precision of weight function technique, (iii) modeling relevant geometries using the finite element method (FEM), (iv) working on the implementation of direct stress intensity factor K determination in the Higher Order Displacement Discontinuity Method (HODDM), and (v) developing tools to deal with residual stress fields around the boundary of the hydraulically pressurized boreholes.

The maintenance of aircraft structure with lower cost is one of the prime concerns to regulatory authorities. The carbon fiber-reinforced polymer (CFRP) patches are widely used to repair the cracked structure. The demands and application of CFRP compel its price to increase in the near future. A distinct perspective of repairing the cracked aluminum panel with the hybrid composite patch is presented in this paper. The purpose of this paper is to propose an alternative patch material in the form of a hybrid composite patch which can provide economical repair solution.

The patch hybridization is performed by preparing the hybrid composite from tows of carbon fiber and glass fiber. Rule of hybrid mixture and modified Halpin–Tsai’s equation are used to evaluate the elastic constant. The stress intensity factor and interfacial stresses are determined using finite element analysis. The debonding initiation load is evaluated after testing under mode-I loading condition.

The hybrid composite patch has rendered the adequate performance for reduction of stress intensity in the cracked panel and control of interfacial stresses in the adhesive layer. The repair efficiency and repair durability of the composite patch repair was ensured by incorporation of the hybrid composite patch.

The studies involving patch hybridization for the application of composite patch repair are presently lacking. The influence of the patch stiffness, methodology to prepare the hybrid composite patch and effects of hybridization on the performance of composite patch repair is presented in this paper.

The purpose of this paper is to present the determination of critical stress intensity factor (K_C) both by experimental method and three-dimensional (3D) finite element simulations.

CT specimens of different compositions of Al6061-TiC composites (3wt%, 5wt% and 7wt% TiC) with variable crack length to width (a/W=0.3-0.6) ratios are machined from as-cast composite block. After fatigue pre-cracking the specimens to a required crack length, experimental load vs crack mouth opening displacement data are plotted to calculate the K_C value. Elastic 3D finite element simulations have been conducted for CT specimens of various compositions and a/W ratios to compute K_C. The experimental results indicate that the magnitude of K_C depends on a/W ratios, and significantly decreases with increase in a/W ratios of the specimen.

From 3D finite element simulation, the K_C results at the centre of CT specimens for various Al6061-TiC composites and a/W ratios show satisfactory agreement with experimental results compared to the surface.

The research work contained in this manuscript was conducted during 2015-2016. It is original work except where due reference is made. The authors confirm that the research in their work is original, and that all the data given in the article are real and authentic. If necessary, the paper can be recalled, and errors corrected.

The main aim of this study is to investigate the mixed-mode I/II failure and the cracking manner of three-dimensional (3D)-printed components made by the fused deposition modeling technique in an experimental and theoretical manner.

Acrylonitrile butadiene styrene (ABS) material and a modified printing method (that increases the adhesion and integrity between the layers and strands) are used for manufacturing the semicircular bending (SCB) test samples. In addition to precracking, the effect of additional stress concentration on the stress field is studied by introducing three small holes to the SCB fracture samples. The critical mixed-mode I/II failure loads obtained from the experiments are predicted using different stress/strain-based fracture theories, including maximum tangential stress (MTS), maximum tangential strain (MTSN), generalized form of MTS and MTSN and combination of them with equivalent material concept (EMC). The effects of plastic deformation, as well as the structural stress concentration, are considered for a more realistic prediction of mixed-mode fracture load.

The stress-based criteria are more suitable than the strain-based theories. Among the investigated fracture models, the EMC–generalized maximum tangential stress theory provided the best agreement with the experimental results obtained from 3D-printed SCB tests.

The influences of stress risers and applicability of different failure theories in cracked layered 3D-printed parts are studied on the fracture behavior of tested specimens under mixed-mode I/II.

The purpose of this paper is to introduce the double-periodic lattice, composed of bending-resistant fibers. The essence of the model is that the filaments are of infinite length and withstand tension and bending. The constitutive equations of the lattice in discrete and differential formulations are derived. Two complementary systems of loads, which cause different deformation two orthogonal families of fibers, occur in the lattice. The fracture behavior of the material containing a semi-infinite crack is investigated. The crack problem reduces to the exactly solvable Riemann-Hilbert problem. The solution demonstrates that the behavior of material cardinally depends upon the tension in the orthogonal family of fibers. If tension in fibers exists, opening of the crack under action of loads in two-dimensional lattice is similar to those in elastic solid. In the absence of tension, contrarily, there is a finite angle between edges at the crack tip.

The description of stress state in the crack vicinity is reduced to the solution of mixed boundary value problem for simultaneous difference equations. In terms of Fourier images for unknown functions the problem is equivalent to a certain Riemann-Hilbert problem.

The analytical solution of the problem shows that fracture behavior of the material depends upon the presence of stabilizing tension in fibers, parallel to crack direction. In the presence of tension in parallel fibers fracture character of two-dimensional lattice is similar to behavior of elastic solid. In this case the condition of crack grows can be formulated in terms of critical stress intensity factor. Otherwise, in the absence of stabilizing tension, the crack surfaces form a finite angle at the tip.

Linear behavior of fibers until rupture. Small deflections. Perfect two-dimensional lattice.

The model provides exact analytical estimation of stresses on the crack tip as the function of fibers’ stiffness.

The model is the extension of known lattice models, taking into account the semi-infinite crack in the lattice. This is the first known closed form solution for an infinite lattice model with the crack.

Acrylonitrile butadiene styrene (ABS), as a light and high strength thermoplastic polymer, has found extensive applications in different industries. Fused filament fabrication, known as three-dimensional (3D) printing technique is considered a rapid prototyping technique that is frequently applied for production of samples of ABS material. Therefore, the purpose of this study is to investigate the mechanical and fracture behavior of such materials and the techniques to improve such properties.

Experimental and numerical analyses have been conducted to investigate the effects of internal architecture and chopped carbon fiber (CF) fillers on the mechanical properties and mixed mode fracture behavior of the ABS samples made by 3D printing technique. Four different filling types at 70% filling ratios have been used to produce tensile and special fracture test samples with pure and CF filled ABS filaments (CF-ABS) using 3D process. A special fixture has been developed to apply mixed mode loading on fracture samples, and finite element analyses have been conducted to determine the geometric function of such samples at different loading angles.

It has been determined that the printing pattern has a significant effect on the mechanical properties of the sample. The addition of 15% CF to pure ABS resulted in a significant increase in tensile strength of 46.02% for line filling type and 15.04% for hexagon filling type. It has been determined that as the loading angle increases from 0° to 90°, the KIC value decreases. The addition of 15% CF increased the K_IC values for hexagonal and line filling type by 64.14% and 12.5%, respectively.

The damage that will occur in ABS samples produced in 3D printers depends on the type, amount, filling speed, filling type, filling ratio, filling direction and mechanical properties of the additives. All these features are clearly dependent on the production method. Even if the same additive is used, the production method difference shows different microstructural parameters, especially different mechanical properties.

Determining fiber orientations around geometric discontinuities is challenging and simultaneously crucial when designing laminates against failure. The purpose of this paper is to present an approach for selecting the fiber orientations in the vicinity of a geometric discontinuity; more specifically round holes with edge cracks. Maximum stresses in the discontinuity region are calculated using Classical Lamination Theory (CLT) and the stress concentration factor for the aforementioned condition. The minimum moment to cause failure in a lamina is estimated using the Tsai–Hill and Tsai–Wu failure theories for a symmetric general stacking laminate. Fiber orientations around the discontinuity are obtained using the Tsai–Hill failure theory.

The current research focuses on a general stacking sequence laminate under three-point bending conditions. The laminate material is S2 fiber glass/epoxy. The concepts of mode I stress intensity factor and plastic zone radius are applied to decide the radius of the plastic zone, and stress concentration factor that multiplies the CLT stress distribution in the vicinity of the discontinuity. The magnitude of the minimum moment to cause failure in each ply is then estimated using the Tsai–Hill and Tsai–Wu failure theories, under the aforementioned stress concentration.

The findings of the study are as follows: it confirms the conclusions of previous research that the size and shape of the discontinuity have a significant effect on determining such orientations; the dimensions of the laminate and laminae not only affect the CLT results, but also the effect of the discontinuity in these results; and each lamina depending on its position in the laminate will have a different minimum load to cause failure and consequently, a different fiber orientation around the geometric discontinuity.

This paper discusses an important topic for the manufacturing and design against failure of Glass Fiber Reinforced Plastic (GFRP) laminated structures. The topic of introducing geometric discontinuities in unidirectional GFRP laminates is still a challenging one. This paper addresses these issues under 3pt bending conditions, a load condition rarely approached in literature. Therefore, it presents a fairly simple approach to strengthen geometric discontinuity regions without discontinuing fibers.

This study aims to comprehensively investigate the mixed-mode fracture behavior and mechanical properties of selective laser sintering (SLS) polyamide 12 (PA12) components, considering different build orientations and layer thicknesses. The primary objectives include the following. Conducting mixed-mode fracture and mechanical analyses on SLS PA12 parts. Investigating the influence of build orientation and layer thickness on the mechanical properties of SLS-printed components. Examining the fracture mechanisms of SLS-produced Arcan fracture and tensile specimens through experimental methods and finite element analyses.

The research used a combination of experimental techniques and numerical analyses. Tensile and Arcan fracture specimens were fabricated using the SLS process with varying build orientations (X, X–Y, Z) and layer thicknesses (0.1 mm, 0.2 mm). Mechanical properties, including tensile strength, modulus of elasticity and critical stress intensity factor, were quantified through experimental testing. Mixed-mode fracture tests were conducted using a specialized fixture, and finite element analyses using the J-integral method were performed to calculate fracture toughness. Scanning electron microscopy (SEM) was used for detailed morphological analysis of fractured surfaces.

The investigation revealed that the highest tensile properties were achieved in samples fabricated horizontally in the X orientation with a layer thickness of 0.1 mm. Additionally, parts manufactured with a layer thickness of 0.2 mm exhibited favorable mixed-mode fracture behavior. The results emphasize the significance of build orientation and layer thickness in influencing mechanical properties and fracture behavior. SEM analysis provided valuable insights into the failure mechanisms of SLS-produced PA12 components.

This study contributes to the field of additive manufacturing by providing a comprehensive analysis of the mixed-mode fracture behavior and mechanical properties of SLS-produced PA12 components. The investigation offers novel insights into the influence of build orientation and layer thickness on the performance of such components. The combination of experimental testing, numerical analyses and SEM morphological observations enhances the understanding of fracture behavior in additive manufacturing processes. The findings contribute to optimizing the design and manufacturing of high-quality PA12 components using SLS technology.

The determination of mode-I fracture toughness of brittle structural materials by means of the notched Brazilian disc configuration is studied. Advantage is taken of a recently introduced analytical solution and, also, of data provided by an experimental protocol with notched marble specimens under diametral compression using the loading device suggested by International Society for Rock Mechanics (ISRM) and also the three-dimensional digital image correlation (3D-DIC) technique.

The analytical solution highlighted the role of geometrical factors, like, for example, the width of the notch, which are usually disregarded. The data of the experimental protocol were comparatively considered with those concerning the response of the specific material under uniaxial tensile load.

This combined study provided interesting data concerning some open issues, as it is the exact crack initiation point and the level of the critical load causing crack initiation. It was definitely indicated that the crack initiation point is not a priori known (even for notched specimens) and, also, that the maximum recorded load does not correspond by default to the critical load responsible for the onset of catastrophic macroscopic fracture.

It was suggested that the load considered critical one for the determination of mode-I fracture toughness K_IC is erroneous. At a load equal to about 70% of the maximum one, a process zone is formed (zone of non-reversible phenomena) around the notch's crown, designating termination of the validity of any linear elastic solution used to determine the normalized stress intensity factors (SIFs). Moreover, at a load level equal to about 95% of the macroscopically observed fracture load, crack propagation has already begun. Therefore, the experimental procedure must be monitored with additional equipment, providing an overview of the displacement field developed during loading.

This study aims to predict the fracture properties of geopolymer concrete, which is necessary for studying failure behaviour of concrete.

Geopolymers are new alternative binders for cement in which polymerization gives strength to concrete rather than through hydration. Geopolymer concrete was developed from industrial byproducts such as GGBS and dolomite. Present study estimates the fracture energy of GGBS geopolymer concrete using three point bending test (RILEM TC50-FMC) with different percentages of dolomite and compare with cement concrete having same strength.

The fracture properties such as peak load, critical stress intensity factor, fracture energy and characteristic length are found to be higher for GGBS-dolomite geopolymer concrete, when their proportion becomes 70:30.

To the best of the authors’ knowledge, this is an original experimental work.