The author discusses the resistance of metal to the propagation of cracks, and points out that in the accepted method of fatigue testing the results are not conclusive because there is no distinction between (1) the load and the number of repeated stresses required to start cracks and (2) the load and the number of reversals needed to propagate the cracks to failure. The investigation reported in the paper was undertaken to determine ( a ) the stress and number of reversals required to start a fatigue crack, and ( b ) the resistance of the material to the effect of a fatigue crack once it had been formed. The tests reported were conducted on annealed cold-rolled low-carbon steel bars with various finishes. The author presents data on the rate of progress of the cracks and on the size of the cracks, the latter of which was determined by magnetizing the bars and inspecting them with finely divided iron oxide in a bath of kerosene.

Architectured materials contain highly controlled structures and morphological features at length scales intermediate between the microscale and the size of the component. In dense architectured materials, stiff building blocks of well-defined size and shape are periodically arranged and bonded by weak but deformable interfaces. The interplay between the architecture of the materials and the interfaces between the blocks can be tailored to control the propagation of cracks while maintaining high stiffness. Interestingly, natural materials such as seashells, bones, or teeth make extensive use of this strategy. While their architecture can serve as inspiration for the design of new synthetic materials, a systematic exploration of architecture-property relationships in architectured materials is still lacking. In this study, we used the discrete element method (DEM) to explore the fracture mechanics of several hundreds of 2D tessellations composed of rigid “tiles” bonded by weaker interfaces. We explored crack propagation and fracture toughness in Voronoi-based tessellations (to represent intergranular cracking in polycrystalline materials), tessellations based on regular polygons, and tessellations based on brick-and-mortar. We identified several toughening mechanisms including crack deflection, crack tortuosity, crack pinning, and process zone toughening. These models show that periodic architectures can achieve higher toughness when compared with random microstructures, the toughest architectures are also the most anisotropic, and tessellations based on brick and mortar are the toughest. These findings are size independent and can serve as initial guidelines in the development of new architectured materials for toughness.

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.

Mussel adhesion is a problem of great interest to scientists and engineers. Recent microscopic imaging suggests that the mussel material is porous with patterned void distributions. In this paper, we study the effect of the pore distribution on the interfacial-to-the overall response of an elastic porous plate, inspired from mussel plaque, glued to a rigid substrate by a cohesive interface. We show using a semi-analytical approach that the existence of pores in the vicinity of the crack reduces the driving force for crack growth and increases the effective ductility and fracture toughness of the system. We also demonstrate how the failure mode may switch between edge crack propagation and inner crack nucleation depending on the geometric characteristics of the bulk in the vicinity of the interface. Numerically, we investigate using the finite element method two different void patterns; uniform and graded. Each case is analyzed under displacement-controlled loading. We show that by changing the void size, gradation, or volume fraction, we may control the peak pulling force, maximum elongation at failure, as well as the total energy dissipated at complete separation. We discuss the implications of our results on design of bulk heterogeneities for enhanced interfacial behavior.

Stepwise crack propagation is evidently observed in experiments both in geomaterials and in hydrogels. Pizzocolo et al. (2012, “Mode I Crack Propagation in Hydrogels is Step Wise,” Eng. Fract. Mech., 97 (1), pp. 72–79) show experimental evidence that mode I crack propagation in hydrogel is stepwise. The pattern of the intermittent crack growth is influenced by many factors, such as porosity of the material, the permeability of the fluid, the stiffness of the material, etc. The pause duration time is negatively correlated with the stiffness of the material, while the average propagation length per step is positively correlated. In this paper, we integrate extended finite element method (XFEM) and enhanced local pressure (ELP) method, and incorporate cohesive relation to reproduce the experiments of Pizzocolo et al. in the finite deformation regime. We investigate the stepwise phenomenon in air and in water, respectively, under mode I fracture. Our simulations show that despite the homogeneous material properties, the crack growth under mode I fracture is stepwise, and this pattern is influenced by the hydraulic permeability and the porosity of the material. Simulated pause duration is negatively correlated with stiffness, and the average propagating length is positively correlated with stiffness. In order to eliminate the numerical artifacts, we also take different time increments into consideration. The staccato propagation does not disappear with smaller time increments, and the pattern is approximately insensitive to the time increment. However, we do not observe stepwise crack growth scheme when we simulate fracture in homogeneous rocks.

Swelling and crack propagation in ionized hydrogels plays an important role in industry application of personal care and biotechnology. Unlike nonionized hydrogel, ionized hydrogel swells up to strain of many 1000's %. In this paper, we present a swelling driven fracture model for ionized hydrogel in large deformation. Flow of fluid within the crack, within the medium, and between the crack and the medium are accounted for. The partition of unity method is used to describe the discontinuous displacement field and chemical potential field, respectively. In order to capture the chemical potential gradient between the gel and the crack, an enhanced local pressure (ELP) model is adopted. The capacity of this numerical model to study the fracture and swelling behaviors of ionized gels with low Young's modulus (< 1 MPa) and low permeability (< 10 −16 m 4 /Ns) is demonstrated. Two numerical examples show the performance of the implemented model (1) swelling with crack opening and (2) swelling with crack propagation. Simulations demonstrate that shrinking of a gel results in decreasing macroscopic stress and simultaneously increasing stress at crack tips. Different scales yield opposite responses, underscoring the need for multiscale modelling. While cracking as a result of external loading can be prevented by reducing the overall stress level in the structure, reducing overall stress levels will not result in reducing the crack initiation and propagation due to swelling.

Knowledge of the subcritical crack growth (SCG) in cement-based materials subject to concurrent physical and chemical attacks is of great importance for understanding and mitigating the chemomechanical deterioration in concrete structural members. In this study, the SCG in hardened cement pastes is investigated experimentally by a novel test approach aided with microcharacterization. In the test, specimens of negative geometry are designed, which enable the use of load control to trigger stable crack propagation in hardened cement pastes. Multiple specimens, cast from the same batch of mixture, are exposed to the same chemical condition and loaded at the same age. With the aid of a high-resolution microscopy system, which is used to trace the crack tip, the average trend and the associated variation of the dependence of crack velocity v on the stress intensity factor K at the crack tip are obtained. Different from static fatigue, three distinctive regions are captured in the K–v curves of specimens experiencing chemomechanical deterioration. With the help of advanced techniques including scanning electron microscopy (SEM), atomic-force microscopy (AFM), and Raman spectroscopy, the microstructure destruction and chemical composition change induced by the imposed chemomechanical attack are characterized at different stages. In addition to the physical insights for deeper understanding of the coupled effect of chemomechanical attack, these experimental results provide important macro- and microscopic benchmarks for the theoretical modeling and numerical investigation in the future studies.

Classical dynamic fracture mechanics predicts that the crack branching occurs when crack propagation speed exceeds a subsonic critical velocity. In this paper, we performed simulations on the dynamic fracture behaviors of idealized discrete mass–spring systems. It is interesting to note that a crack does not branch when traveling at supersonic speed, which is consistent with others' experimental observations. The mechanism for the characteristics of crack branching at different propagation speeds is studied by numerical and theoretical analysis. It is found that for all different speed regimes, the maximum circumferential stress near the crack tip determines the crack branching behaviors.

A refined molecular life prediction scheme for single-walled carbon nanotubes (SWCNTs), taking into consideration C–C bond rotation and preexisting strain under mechanical loads, is proposed. The time-dependent fracture behavior of 12 different cases of zigzag (18,0) SWCNT, each embedded with either a single Stone–Wales (SW) defect of different types or two interacting or noninteracting defects, is studied under axially applied tensile load. It is shown that the patterns of atomistic crack propagation and fatigue lives of SWCNTs are influenced by the type and orientation of the SW defect(s), inter-defect distance, as well as the magnitude of externally applied stress. For SWCNTs with two SW defects, if the inter-defect distance is within the so called indifference length, defect-defect interaction does exist, and it has pronounced effects on diminishing the lives of the nanotubes. Also, the defect-defect interaction is stronger at shorter inter-defect distance, resulting in shorter fatigue lives.

Among the many potential two-dimensional carbon allotropes inspired by graphene, graphynes have received exceptional attention recently. Graphynes exhibit remarkable mechanical properties depending on their structure. The similar structure and two-dimensional nature of these materials yield many properties that are similar to those of graphene, but the presence of heterogeneous bond types is expected to lead to distinct properties. The main subject of this work is graphdiyne, one of the few graphynes that has been fabricated in large quantities. In this paper, we perform fracture analysis on graphdiyne and find a delocalized failure mechanism in which a crack propagates along a diagonal with respect its original direction. The covalence of the material allows for this simple but intriguing phenomenon to be investigated. Graphene is also tested to compare the behavior. This mechanism has implications for the toughness and robustness of this material, which is topical for many device applications recently proposed in the literature. Further, connections of such delocalized failure mechanisms are made to that of hidden length and sacrificial bonding in some biological systems such as proteins, bone, and nacre.

A simple analytical theory is proposed for estimating the number of radial cracks which will propagate in brittle materials subjected to axisymmetric transverse surface loads. First, an expression is obtained for the stress intensity factor of a traction-free star-shaped crack in an infinite elastic membrane subjected to axisymmetric transverse loads. Combining this relation with the critical stress intensity factor criterion for fracture, an implicit expression is obtained which defines the number of cracks as a function of the applied loading, initial flaw size, and fracture toughness. Based on the form of this expression, we argue that if the initial flaw size is sufficiently small compared to the length scale associated with the loading, then the number of cracks can be determined approximately in closed-form from the analysis of a traction-free star-shaped crack in a thin body subjected to uniform equibiaxial in-plane tension. In an attempt to validate the theory, comparisons are made with spherical micro-indentation experiments of silicon carbide (Wereszczak and Johanns, 2008, “Spherical Indentation of SiC,” Advances in Ceramic Armor II, Wiley, NY, Chap. 4) and good agreement is obtained for the number of radial cracks as a function of indentation load.

Shales, clays, hydrogels, and tissues swell and shrink under changing osmotic conditions, which may lead to failure. The relationship between the presence of cracks and fluid flow has had little attention. The relationship between failure and osmotic conditions has had even less attention. The aim of this research is to study the effect of osmotic conditions on propagating discontinuities under different types of loads for saturated ionized porous media using the finite element method (FEM). Discontinuous functions are introduced in the shape functions of the FEM by partition of unity method, independently of the underlying mesh. Damage ahead of the crack-tip is introduced by a cohesive zone model. Tensile loading of a crack in an osmoelastic medium results in opening of the crack and high pressure gradients between the crack and the formation. The fluid flow in the crack is approximated by Couette flow. Results show that failure behavior depends highly on the load, permeability, (osmotic) prestress and the stiffness of the material. In some cases it is seen that when the crack propagation initiates, fluid is attracted to the crack-tip from the crack rather than from the surrounding medium causing the crack to close. The results show reasonable mesh-independent crack propagation for materials with a high stiffness. Stepwise crack propagation through the medium is seen due to consolidation, i.e., crack propagation alternates with pauses in which the fluid redistributes. This physical phenomenon challenges the numerical scheme. Furthermore, propagation is shown to depend on the osmotic prestressing of the medium. This mechanism may explain the tears observed in intervertebral disks as degeneration progresses.

Dynamic crack propagation across a perpendicular interface in a glass specimen was investigated to understand the interaction between the crack and the interface under impact loading. The glass specimen was composed of two glass plates in an edge-to-edge configuration with an adhesive layer in between. One of the plates had a notch for a plastic projectile to strike. A single crack developed from the notch tip, and propagated perpendicularly into the interface. The patterns of crack propagation across the interface depend on the adhesive conditions on the interface. Within a range of impact speeds, the crack is arrested at the interface without any adhesive. The crack passes across a firmly bonded interface with little obstruction by the interface. The crack branches into multiple cracks after it passes through a thicker interface filled with adhesive. Projectiles having higher kinetic energies cause more severe crack branching after the crack extends into the second glass plate.

Bone is similar to fiber-reinforced composite materials made up of distinct phases such as osteons (fiber), interstitial bone (matrix), and cement lines (matrix-fiber interface). Microstructural features including osteons and cement lines are considered to play an important role in determining the crack growth behavior in cortical bone. The aim of this study is to elucidate possible mechanisms that affect crack penetration into osteons or deflection into cement lines using fracture mechanics-based finite element modeling. Cohesive finite element simulations were performed on two-dimensional models of a single osteon surrounded by a cement line interface and interstitial bone to determine whether the crack propagated into osteons or deflected into cement lines. The simulations investigated the effect of (i) crack orientation with respect to the loading, (ii) fracture toughness and strength of the cement line, (iii) crack length, and (iv) elastic modulus and fracture properties of the osteon with respect to the interstitial bone. The results of the finite element simulations showed that low cement line strength facilitated crack deflection irrespective of the fracture toughness of the cement line. However, low cement line fracture toughness did not guarantee crack deflection if the cement line had high strength. Long cracks required lower cement line strength and fracture toughness to be deflected into cement lines compared with short cracks. The orientation of the crack affected the crack growth trajectory. Changing the fracture properties of the osteon influenced the crack propagation path whereas varying the elastic modulus of the osteon had almost no effect on crack trajectory. The findings of this study present a computational mechanics approach for evaluating microscale fracture mechanisms in bone and provide additional insight into the role of bone microstructure in controlling the microcrack growth trajectory.

This paper deals with the dissipation associated with quasistatic microcracking of brittle materials exhibiting softening behavior. For this purpose an elastodamaging cohesive zone model is used, in which cohesive tractions decrease (during crack propagation) with increasing displacement discontinuities. Constant cohesive tractions are included in the model as a limiting special case. Considering a representative volume element containing a dilute distribution of many parallel microcracks, we quantify energy dissipation associated with mode I microcrack propagation. This is done in the framework of thermodynamics, without restricting assumptions on the size of the cohesive zones. Model predictions are compared with exact solutions, which are accessible for constant cohesive tractions. The proposed model reliably predicts both onset of crack propagation and the dissipation during microcracking. It is shown that the energy release rate is virtually equal to the area under the softening curve, if the microscopic tensile strength is at least twice as large as the macroscopic tensile strength. This result justifies approaches relying on the concept of constant energy release rate, such as those frequently used in the engineering practice.

In this paper, we present a fracture-mechanics based model, the so-called bridged crack model ( Carpinteri, A., 1981, “A Fracture Mechanics Model for Reinforced Concrete Collapse,” Proc. of IABSE Colloquium on Advanced Mechanics of Reinforced Concrete, Delft, I.A.B.S.E., Zürich, pp. 17–30 ; Carpinteri, A., 1984, “Stability of Fracturing Process in R.C. Beams,” J. Struct. Engng. (A.S.C.E.), 110, pp. 544–558 ) for the analysis of brittle matrix composites with discontinuous ductile reinforcements under the condition of repeated bending loading. In particular, we address the case of composites with very high number of reinforcements (i.e., fiber-reinforced composites, rather than conventionally reinforced concrete). With this aim, we propose a new iterative procedure and compare it to the algorithm recently proposed by Carpinteri, Spagnoli, and Vantadori (2004, “A Fracture Mechanics Model for a Composite Beam with Multiple Reinforcements Under Cyclic Bending,” Int. J. Solids Struct., 41, pp. 5499–5515) , showing the advantages in terms of computational efficiency. Furthermore, we analyze the combined effects of crack length, brittleness number, and fiber number on the cyclic behavior of the composite beam, showing the conditions enhancing the energy dissipation in the composite system. Eventually, we analyze crack propagation and propose, consistently with the model premises, a fracture-mechanics-based crack propagation criterion that allows one to simulate cyclic bending tests under the fixed grip condition.

The paper is devoted to formulation and analysis of a new model of structural fatigue that is a direct extension of the model of contact fatigue developed by Kudish (2000, STLE Tribol. Trans., 43, pp. 711–721 ). The model is different from other published models of structural fatigue ( Collins, J. A., 1993, Failure of Materials and Mechanical Design: Analysis, Prediction, Prevention, 2nd ed., Wiley, New York ) in a number of aspects such as statistical approach to material defects, stress analysis, etc. The model is based on fracture mechanics and fatigue crack propagation. The model takes into account local stress distribution, initial statistical distribution of defects versus their size, crack location, and orientation, and material fatigue resistance parameters. The assumptions used for the new model derivation are stated clearly and their validity is discussed. The model considers the kinetics of crack distribution by taking into account the fact that the crack distribution varies with the number of applied loading cycles due to crack growth. A qualitative and quantitative parametric analysis of the model is performed. Some analytical formulas for fatigue life as a function of the initial defect distribution, material fatigue resistance, and stress state are obtained. Examples of application of the model to predicting fatigue of beam bending and torsion and contact fatigue for tapered bearings is presented.

A cohesive interface element is presented for the finite element analysis of crack growth in thin specimens. In this work, the traditional cohesive interface model is extended to handle cracks in the context of three-dimensional shell elements. In addition to the traction-displacement law, a bending moment-rotation relation is included to transmit the moment and describe the initiation and propagation of cracks growing through the thickness of the shell elements. Since crack initiation and evolution are a natural outcome of the cohesive zone model without the need of any ad hoc fracture criterion, this model results in automatic prediction of fracture. In particular, this paper will focus on cases involving mode I/III fracture and bending, typical of complex cases existing in industrial applications in which thin-walled structures are subjected to extreme loading conditions (e.g., crashworthiness analysis). Finally, we will discuss how the three-dimensional effects near the crack front may affect the determination of the cohesive parameters to be used with this model.

In this paper a general study on tubular adhesive joint under axial load is presented. We focus our attention on both static and dynamic behavior of the joint, including shear and normal stresses and strains in the adhesive layer, joint optimization, failure load for brittle crack propagation, and crack detection based on free vibrations. First, we have considered the shear and normal stresses and strains in the adhesive layer to propose an optimization to uniform axial strength (UAS) and to reduce the stress peaks in the bond. The stress analysis confirms that the maximum shear stresses are attained at the ends of the adhesive and that the peak of maximum shear stress is reached at the end of the stiffer tube and does not tend to zero as the adhesive length approaches infinity. A fracture energy criterion to predict brittle crack propagation for conventional and optimized joint is presented. The stability of brittle crack propagation and the strength of the joint, as well as the ductile-brittle failure transition, are analyzed. A detection method to predict crack severity, based on joint dynamic behavior, is also proposed. The crack detection is achieved through the determination of the axial natural frequencies of the joint as a function of the crack length, by determining the roots of a determinantal equation.

In Part I of this series, we have obtained the fundamental solution for a mode II intersonic crack which involves a crack moving uniformly at a velocity between the shear and longitudinal wave speeds while subjected to a pair of concentrated forces suddenly appearing at the crack tip and subsequently acting on the crack faces. The fundamental solution can be used to generate solutions for intersonic crack propagation under arbitrary initial equilibrium fields. In this paper, Part II of this series, we study a mode II crack suddenly stopping after propagating intersonically for a short time. The solution is obtained by superposing the fundamental solution and the auxiliary problem of a static crack emitting dynamic dislocations such that the relative crack face displacement in the fundamental solution is negated ahead of where the crack tip has stopped. We find that, after the crack stops moving, the stress intensity factor rapidly rises to a finite value and then starts to change gradually toward the equilibrium value for a static crack. A most interesting feature is that the static value of stress intensity is reached neither instantaneously like a suddenly stopping subsonic crack nor asymptotically like a suddenly stopping edge dislocation. Rather, the dynamic stress intensity factor changes continuously as the shear and Rayleigh waves catch up with the stopped crack tip from behind, approaches negative infinity when the Rayleigh wave arrives, and then suddenly assumes the equilibrium static value when all the waves have passed by. This study is an important step toward the study of intersonic crack propagation with arbitrary, nonuniform velocities.