Crack Propagation Speed Research Articles

A Simple Model of Dynamic Cleavage Producing Constant Speed Crack Propagation in a Sample of Finite Width

A simple model of dynamic cleavage under longitudinal shear deformation is analyzed as an attempt to understand how ancient lapidaries might have produced smooth cleaved surfaces. Attention is concentrated on the time signature of the load applied to the specimen in order to maintain a constant stress intensity factor (or energy release rate) at the crack tip as it propagates away from the location of the applied load at a constant speed. The analysis is also applicable to situations in which fracture requires a time dependent energy release rate. An example of the cleavage of diamond is considered.

Fatigue characterization of Poly Vinyl Chloride (PVC) foam core sandwich composite using the G-control method

This paper presents experimental results from cyclic crack propagation tests performed on sandwich specimens with glass/epoxy face sheets and Poly Vinyl Chloride (PVC) foam cores using the G-controlled cyclic energy release rate (ΔG) test procedure. The face material was tested in tension, compression and shear to determine in-plane and out-of-plane mechanical properties, such as Young’s modulus, Poisson’s ratio and shear modulus. These properties were then used in an analytical model of the mixed-mode bending sandwich specimen to calculate compliance and energy release rate. Finite element analysis was used to determine the mode-mixity of the crack loading. Experimental crack growth cyclic tests were carried out on pre-cracked mixed-mode bending sandwich specimens with H45, H100 and H160 PVC foam cores under two mode-mixities (mode I and mode II dominant). Post-mortem analysis was performed on tested specimens, highlighting the influence of mode mixity and foam density on the crack path. Crack propagation diagrams showing da/dN versus ΔG curves were obtained to establish the Paris-Erdogan relation for each material combination tested at the two mode-mixities. Results showed constant crack growth rates for all the materials tested and revealed the influence on mode-mixity on crack propagation speed and foam density (higher foam density, slower crack propagation).

Velocidade de Propagação de Trinca por Fadiga de Soldas Subaquáticas Molhadas: Avaliação Fora da Água

Resumo As características de propagação de trinca por fadiga de soldas produzidas em condições convencionais (Soldas feitas fora da agua) e de reparo subaquáticas (Solda subaquática molhada) foram avaliadas fora da agua. As velocidades de crescimento da trinca por fadiga da/dN mostraram uma sensível dependência com a densidade e distribuição de poros, fatores que variam significativamente com o processo de soldagem e meio ambiente. Variações na velocidade de propagação da trinca por fadiga foram correlacionadas com a análise da superfície de fratura na zona de propagação estável da trinca. Os resultados deste estudo mostram que o procedimento de soldagem subaquática molhada produz metal de solda resistente à fadiga que é adequado para uso em baixas tensões aplicadas em estruturas offshore.

A relation between a dynamic fracture model and quasi-static evolution

We study the relations between a dynamic model proposed by Bourdin, Larsen and Richardson, and quasi-static fracture evolution. We assume the dynamic model has the boundary displacements of the material as input, and consider time-rescaled solutions of this model associated to a sequence of boundary conditions with speed going to zero. Next, we study whether this rescaled sequence converges to a function satisfying quasi-static fracture evolution. Under some hypotheses and assuming the speed of crack propagation slows down following the deceleration of boundary displace- ments, our main result shows that (up to a subsequence) the rescaled solutions converge to a quasi-static evolution.

Universal hydrofracturing algorithm for shear-thinning fluids: Particle velocity based simulation

A universal particle velocity based algorithm for simulating hydraulic fractures, previously proposed for Newtonian fluids, is extended to the class of shear-thinning fluids. The scheme is not limited to any particular elasticity operator or crack propagation regime. The computations are based on two dependent variables: the crack opening and the reduced particle velocity. The application of the latter facilitates utilization of the local condition of Stefan type (speed equation) to trace the fracture front. The condition is given in a general explicit form which relates the crack propagation speed (and the crack length) to the solution tip asymptotics. The utilization of a modular structure, and the adaptive character of its basic blocks, result in a flexible numerical scheme. The computational accuracy of the proposed algorithm is validated against a number of analytical benchmark solutions.

Experimental study and theoretical analysis of partially encased continuous composite beams

The mechanical behavior and the law of moment redistribution of the partially encased continuous composite beam (PECCB) are investigated in this paper. One common continuous composite beam and three PECCBs were tested. The main variable parameter of the three PECCB specimens is the amount of longitudinal reinforcement in the concrete slab of hogging moment region. Owing to the contribution of the web encasement, PECCBs have much slower crack propagation speed in the hogging moment region and higher ultimate capacity. The web encasement also contributes to postponing the yielding of the bottom flange, and therefore prevents local buckling in the steel girder. As the amount of reinforcement in the concrete slab of hogging moment region increases, the degree of moment redistribution of PECCBs decreases. On the basis of analyzing the moment redistribution requirement for plastic design and the ultimate rotation capacity of hogging moment section, the required and available moment redistribution factors of PECCBs are obtained. A parameter Rp is introduced to evaluate the relative relationship between the longitudinal reinforcement in the concrete slab and the rest part of the partially encased section, and the value of Rp should be restricted within 0.35 to enable full moment redistribution for plastic design of PECCBs.

High- and low-cycle fatigue influence of silicon, copper, strontium and iron on hypo-eutectic Al–Si–Cu and Al–Si–Mg cast alloys used in cylinder heads

In this publication, ambient condition fatigue investigations with different types of Al–Si–Cu and Al–Si–Mg cast alloys in rotating-bending high-cycle fatigue (HCF) and push–pull low-cycle fatigue (LCF) regimes have been performed with varying Si, Cu, Fe and Sr contents. The cast alloys investigated here are common used in cylinder heads for automotive application. Because the cylinder head is one of the most fatigued parts in combustion chamber engines, the microstructural knowledge of the damage process provides a tool of construction and its material selection. The investigations were also supported with an in-situ microstructural crack observation in high plasticity rotating-bending regimes. The specimens were directly processed out of serial produced T79 heat-treated cylinder heads to provide the equal microstructure for testing as under operational conditions.The observations clearly identified the effects of the individual alloying elements both under low- and high-cycle fatigue. The crack propagation speed and the crack paths were majorly influenced by the eutectic silicon. Additional, the precipitation hardening due to copper affected significantly the fatigue endurance, too. In high plasticities the silicon’s influence got almost lost and only the matrix strength was crucial. Thus, increased fatigue strength in high loaded LCF regimes was observed for alloys with less copper content, thus higher ductility. By contrast, improved HCF and low loaded LCF endurance was only achieved when the matrix strength was increased by copper’s precipitation hardening. Crack branching and deflections strongly influenced the microstructural damage of the ductile AlSi7Mg(Sr) and hence, gained its fatigue strength. Iron phases could not identified as harmful inclusions, since the phases were similar in size of other hard phase elements like the other primary intermetallic phases like Al2Cu and β-Si phases under notch stress aspects, by the well defined solidification process in the test section. Because the crack nucleation mainly occurred on Si particles, strontium as a refinement agent influenced the early crack onset and accordingly the fatigue in total. Thus, the AlSi6Cu4(Sr) had increased lifetimes compared to AlSi6Cu4 both in HCF and LCF. Further, the presented results provide a modification of the Manson–Coffin approach to describe the relationship between plastic strain and lifetime, valid for all proposed alloys with only one set of parameters. Thus, it was possible to perform the fatigue calculation with a reduced range of scatter.

Modeling of crack propagation in weak snowpack layers using the discrete element method

Abstract. Dry-snow slab avalanches are generally caused by a sequence of fracture processes including (1) failure initiation in a weak snow layer underlying a cohesive slab, (2) crack propagation within the weak layer and (3) tensile fracture through the slab which leads to its detachment. During the past decades, theoretical and experimental work has gradually led to a better understanding of the fracture process in snow involving the collapse of the structure in the weak layer during fracture. This now allows us to better model failure initiation and the onset of crack propagation, i.e., to estimate the critical length required for crack propagation. On the other hand, our understanding of dynamic crack propagation and fracture arrest propensity is still very limited. To shed more light on this issue, we performed numerical propagation saw test (PST) experiments applying the discrete element (DE) method and compared the numerical results with field measurements based on particle tracking. The goal is to investigate the influence of weak layer failure and the mechanical properties of the slab on crack propagation and fracture arrest propensity. Crack propagation speeds and distances before fracture arrest were derived from the DE simulations for different snowpack configurations and mechanical properties. Then, in order to compare the numerical and experimental results, the slab mechanical properties (Young's modulus and strength) which are not measured in the field were derived from density. The simulations nicely reproduced the process of crack propagation observed in field PSTs. Finally, the mechanical processes at play were analyzed in depth which led to suggestions for minimum column length in field PSTs.

Low Speed Crack Propagation via Kink Formation and Advance on the Silicon (110) Cleavage Plane.

We present density functional theory based atomistic calculations predicting that slow fracturing of silicon is possible at any chosen crack propagation speed under suitable temperature and load conditions. We also present experiments demonstrating fracture propagation on the Si(110) cleavage plane in the ~100 m/s speed range, consistent with our predictions. These results suggest that many other brittle crystals could be broken arbitrarily slowly in controlled experiments.

Rate dependent fracture of a double cantilever beam with combined bulk and interfacial dissipation

The energy required to fracture viscoelastic media is known to depend on the rate of crack propagation. In this work, crack propagation, driven by applied moments¸ in an idealized model of a viscoelastic double cantilever beam (DCB) is studied. Rate dependency is taken into account through a standard linear solid viscoelastic model for the bulk material, and an adhesive zone model describing bond rupture kinetics for the polymer chains which bridge the interface. Attractive van der Waals (vdW) forces are also taken into account within the adhesive zone. The apparent energy release rate consists of two parts: the energy to overcome adhesion on the interface as well as viscous dissipation in the bulk. The adhesive energy in rupturing polymer chains increases as crack propagation speed increases. Relaxation of the bulk material causes viscous dissipation as stored strain energy is lost. For a beam of fixed length this dissipation was found to be negligible at high and low rates of crack propagation. Between these two limits there is a critical crack propagation speed where viscous dissipation is maximized.

Scenarios of crack propagation in bast fibers: Combining experimental and finite element approaches

This work investigates the rupture of bast fiber type from hemp, to attain better control over the ultimate tensile and fracture strength properties of hemp composites. Crack propagation in both individualized and bundles of hemp fibers is studied. Crack initiation is controlled using generated defects within fibers. A non-contact-ablation apparatus creates these defects using a laser beam directed by high-precision optics. V- and U-type notches are processed, with sizes ranging from 2 to 30μm in depth. The micromechanical testing of damaged fibers is coupled to a high-speed camera, allowing for the measurement of ultimate properties as well as monitoring of the crack propagation.Finite element simulation is developed to identify possible damage scenarios for bundles and elementary fibers. Microcracks are allowed to initiate, grow and coalesce based on non-prescribed crack propagation (i.e., not imposed or with direction update) and stress criteria. High speed camera recording indicate a wide variability in crack propagation speed in the range 2–149m/s. Both longitudinal and transverse cracking are observed depending on the notch geometry. Our results demonstrate that the damage kinetics is a combination of growth and coalescence of microcracks. These damage mechanisms compete depending on the notch geometry and fiber element dimensions.

A peridynamic model for dynamic fracture in functionally graded materials

We introduce a peridynamic model for functionally graded materials (FGMs) and study their dynamic fracture behavior. After verification of elastic wave propagation in FGMs and comparisons with analytical results for the classical model, we analyze dynamic fracture of a functionally graded plate with monotonically varying volume fraction of reinforcement. Mixed-mode loading is imparted by eccentric impact relative to a pre-crack. We study the influence of material gradients, elastic waves, and of contact time and magnitude of impact loading on the fracture behavior in terms of crack path geometry and crack propagation speed. The peridynamic simulations agree very well, through full failure, with experiments. The model leads to a better understanding of how cracks propagate in FGMs and of the factors that control crack path and its velocity in these materials. We discover an interesting effect that surface waves far from the crack tip have in “attracting” the crack towards their location. We discuss advantages offered by the peridynamic model in dynamic fracture of FGMs compared with, for example, FEM-based models.

Effects of void–crack interaction and void distribution on crack propagation in single crystal silicon

Interaction between crack and pre-existing voids in single crystal silicon has been investigated by performing molecular dynamics simulation. It is found that the presence of a single void, ahead of crack tip, can affect the crack propagation through crack–void interaction in one-void model. As the crack–void ligament distance gradually approaches the critical distance, the crack propagation speed decreases. For two-void model, crack propagation behaviors can be substantially influenced by voids distributions (voids aligned along or perpendicular to crack line) under different crack retarding mechanisms, indicating that the distribution of voids provides a prominent role in blocking the crack propagation.

Hydraulic fracture revisited: Particle velocity based simulation

We develop a new effective mathematical formulation and resulting universal computational algorithm capable of tackling various HF models in the framework of a unified approach. The scheme is not limited to any particular elasticity operator or crack propagation regime. Its basic assumptions are: (i) proper choice of independent and dependent variables (with the direct utilization of a new one – the reduced particle velocity), (ii) tracing the fracture front by use of the Stefan condition (speed equation), which can be integrated in closed form and provides an explicit relation between the crack propagation speed and the coefficients in the asymptotic expansion of the crack opening, (iii) proper regularization techniques, (iv) improved temporal approximation, (v) modular algorithm architecture. The application of the new dependent variable, the reduced particle velocity, instead of the usual fluid flow rate, facilitates the computation of the crack propagation speed from the local relation based on the speed equation. This way, we avoid numerical evaluation of the undetermined limit of the product of fracture aperture and pressure gradient at the crack tip (or alternatively the limit resulting from ratio of the fluid flow rate and the crack opening), which always poses a considerable computational challenge. As a result, the position of the crack front is accurately determined from an explicit formula derived from the speed equation. This approach leads to a robust numerical scheme. Its performance is demonstrated using classical examples of 1D models for hydraulic fracturing: PKN and KGD models under various fracture propagation regimes. Solution accuracy is verified against dedicated analytical benchmarks and other solutions available in the literature. The scheme can be directly extended to more general 2D and 3D cases.

Dynamic conducting crack propagation in piezoelectric materials: Mode-II problem

This paper studies the dynamic conducting crack propagation in piezoelectric solids under suddenly in-plane shear loading. Based on the integral transform methods and the Wiener-Hopf technique, the resulting mixed boundary value problem is solved. The analytical solutions of the dynamic stress intensity factor and dynamic electric displacement intensity factor for the Mode II case are derived. Furthermore, the numerical results are presented to illustrate the characteristics of the dynamic crack propagation. It is shown that the universal functions for the dynamic stress and electric displacement intensity factors vanish if the crack propagation speed equals the generalized Rayleigh speed. The results indicate that the defined electro-mechanical coupling coefficient is of great importance to the universal functions and stress intensity factor history.

Numerical and experimental investigation of the cold expansion process with split sleeve in titanium alloy TC4

A series of uniaxial fatigue tests were carried out using specimens containing non-cold expanded and cold expanded holes to assess the effect of split sleeve cold expansion on fatigue behavior of titanium alloy TC4. The fracture surfaces of specimens were observed by scanning electron microscope (SEM). 3D finite element models were also used to analyze the residual stress fields around cold expanded holes. Based on the qualitative finite element analysis (FEA), the multi-axial fatigue lives of the non-cold and cold expanded holes have been predicted by Smith–Watson–Topper (SWT) method and Wang–Brown (WB) method respectively. The effects of the friction between the split sleeve and the hole’s surface were also considered. The results reveal that crack of cold expanded specimen always initiates near entrance face and the crack propagation speed along transverse direction is faster than along axial direction. The lowest compressive stress occurs at the entrance face where crack is preferentially initiated. The mandrel entrance face is the most sensitive region to friction between the split sleeve outer surface and the hole. After cold expansion, fatigue life of TC4 open hole was increased to 1.7–2.2 times. Compared with the result of SWT theory, the result of WB theory is more conservative and reliable.

Continuum shape sensitivity analysis and what-if study for two-dimensional multi-scale crack propagation problems using bridging scale decomposition

This paper presents a shape sensitivity analysis and what-if study for two-dimensional multi-scale crack propagation problems using bridging scale decomposition. The sensitivity equations are derived in a continuum setting using direct differentiation method based on a continuum variational formulation of the bridging scale. Due to the fact that the crack propagation speed in an atomistic simulation is discrete in design, and cannot be formulated as a continuous function of shape design variables, we propose a hybrid method that combines analytical sensitivity analysis with finite difference approach. The finite difference part of the sensitivity analysis is only intended for calculating the sensitivity of crack growth speed based on the analytically obtained sensitivity coefficients of structural responses. The theoretical development on sensitivity formulation in this paper extends the application of the method to irregular-shaped finite elements and general design velocity fields. Furthermore, we evaluate and compare several performance measures that quantify crack propagation speed based on crack tip locations for sensitivity analysis and ultimately for structural optimization. A two-dimensional beam example is used to verify the accuracy of the proposed sensitivity approach. It is also demonstrated through a what-if study that with an adequate performance measure, the impact of macroscopic shape changes on microscopic crack propagation speed can be accurately predicted.

Crack Branching Characteristics at Different Propagation Speeds: From Quasi-Static to Supersonic Regime

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.

Studies on Establishing a Methodology for Predicting the Riveted Joints Fatigue Durability in Aircraft Structures

In this paper are described fatigue physical tests that were performed on a great number of riveted specimens with different constructive and technological parameters. Some of the purposes of the experimental tests, they were: determining the number of load cycles at which cracks by fatigue occurred, determining the moment of initiation, the location and propagation speed of the fatigue crack. For fatigue crack evolution study numerical models were designed. A simplified model for FEM analysis was proposed that reduced considerable the calculus effort and allows models for complex riveted joints. From the described experiments on specimens and numerical simulations there are some important conclusions regarding the fatigue phenomenon in riveted joints such as: important peculiarity of damage by multiple cracks is the cracks junction of adjacent rivet holes, which contributes, by jumping, to increase the degradation rate of assembly; the riveted joint model can be applied with good accuracy to estimate the durability of the structures inclusively to identify and prevent the cases of widespread fatigue damage.

Intersonic delamination in curved thick composite laminates under quasi-static loading

Dynamic delamination in curved composite laminates is investigated experimentally and numerically. The laminate is 12-ply graphite/epoxy woven fabric L-shaped laminate subject to quasi-static loading perpendicular to one arm. Delamination initiation and propagation are observed using high speed camera and load–displacement data is recorded. The quasi-static shear loading initiates delamination at the curved region which propagates faster than the shear wave speed of the material, leading to intersonic delamination in the arms. In the numerical part, the experiments are simulated with finite element analysis and a bilinear cohesive zone model. Cohesive interface elements are used between all plies with the interface properties obtained from tests. The simulations predict a single delamination initiating at the corner under pure mode-I stress field propagating to the arms under pure mode-II stress field. The crack tip speeds transition from sub-Rayleigh to intersonic in conjunction with mode change. In addition to intersonic mode-II delamination, shear Mach waves emanating from the crack tips in the arms are observed. The simulations and experiments are found to be in good agreement at the macro-scale, in terms of load-displacement behavior and failure load, and at the meso-scale, in terms of delamination initiation location and crack propagation speeds. Finally, a mode dependent crack tip definition is proposed and observation of vibrations during delamination is presented. This paper presents the first conclusive evidence of intersonic delamination in composite laminates triggered under quasi-static loading.