Showing papers on "Fracture mechanics published in 2006"

Statistical models of fracture

Abstract: Disorder and long-range interactions are two of the key components that make material failure an interesting playfield for the application of statistical mechanics. The cornerstone in this respect has been lattice models of the fracture in which a network of elastic beams, bonds, or electrical fuses with random failure thresholds are subject to an increasing external load. These models describe on a qualitative level the failure processes of real, brittle, or quasi-brittle materials. This has been particularly important in solving the classical engineering problems of material strength: the size dependence of maximum stress and its sample-to-sample statistical fluctuations. At the same time, lattice models pose many new fundamental questions in statistical physics, such as the relation between fracture and phase transitions. Experimental results point out to the existence of an intriguing crackling noise in the acoustic emission and of self-affine fractals in the crack surface morphology. Recent advances ...

From brittle to ductile fracture of bone

Abstract: Toughness is crucial to the structural function of bone. Usually, the toughness of a material is not just determined by its composition, but by the ability of its microstructure to dissipate deformation energy without propagation of the crack. Polymers are often able to dissipate energy by viscoplastic flow or the formation of non-connected microcracks. In ceramics, well-known toughening mechanisms are based on crack ligament bridging and crack deflection. Interestingly, all these phenomena were identified in bone, which is a composite of a fibrous polymer (collagen) and ceramic nanoparticles (carbonated hydroxyapatite). Here, we use controlled crack-extension experiments to explain the influence of fibre orientation on steering the various toughening mechanisms. We find that the fracture energy changes by two orders of magnitude depending on the collagen orientation, and the angle between collagen and crack propagation direction is decisive in switching between different toughening mechanisms.

Application of Fracture Mechanics Concepts to Hierarchical Biomechanics of Bone and Bone-like Materials

Abstract: Fracture mechanics concepts are applied to gain some understanding of the hierarchical nanocomposite structures of hard biological tissues such as bone, tooth and shells. At the most elementary level of structural hierarchy, bone and bone-like materials exhibit a generic structure on the nanometer length scale consisting of hard mineral platelets arranged in a parallel staggered pattern in a soft protein matrix. The discussions in this paper are organized around the following questions: (1) The length scale question: why is nanoscale important to biological materials? (2) The stiffness question: how does nature create a stiff composite containing a high volume fraction of a soft material? (3) The toughness question: how does nature build a tough composite containing a high volume fraction of a brittle material? (4) The strength question: how does nature balance the widely different strengths of protein and mineral? (5) The optimization question: Can the generic nanostructure of bone and bone-like materials be understood from a structural optimization point of view? If so, what is being optimized? What is the objective function? (6) The buckling question: how does nature prevent the slender mineral platelets in bone from buckling under compression? (7) The hierarchy question: why does nature always design hierarchical structures? What is the role of structural hierarchy? A complete analysis of these questions taking into account the full biological complexities is far beyond the scope of this paper. The intention here is only to illustrate some of the basic mechanical design principles of bone-like materials using simple analytical and numerical models. With this objective in mind, the length scale question is addressed based on the principle of flaw tolerance which, in analogy with related concepts in fracture mechanics, indicates that the nanometer size makes the normally brittle mineral crystals insensitive to cracks-like flaws. Below a critical size on the nanometer length scale, the mineral crystals fail no longer by propagation of pre-existing cracks, but by uniform rupture near their limiting strength. The robust design of bone-like materials against brittle fracture provides an interesting analogy between Darwinian competition for survivability and engineering design for notch insensitivity. The follow-up analysis with respect to the questions on stiffness, strength, toughness, stability and optimization of the biological nanostructure provides further insights into the basic design principles of bone and bone-like materials. The staggered nanostructure is shown to be an optimized structure with the hard mineral crystals providing structural rigidity and the soft protein matrix dissipating fracture energy. Finally, the question on structural hierarchy is discussed via a model hierarchical material consisting of multiple levels of self-similar composite structures mimicking the nanostructure of bone. We show that the resulting “fractal bone”, a model hierarchical material with different properties at different length scales, can be designed to tolerate crack-like flaws of multiple length scales.

Prediction of in situ strengths and matrix cracking in composites under transverse tension and in-plane shear

Abstract: A criterion for matrix failure of laminated composite plies in transverse tension and in-plane shear is developed by examining the mechanics of transverse matrix crack growth. Matrix cracks are assumed to initiate from manufacturing defects and can propagate within planes parallel to the fiber direction and normal to the ply mid-plane. Fracture mechanics models of cracks in unidirectional laminates, embedded plies and outer plies are used to determine the onset and direction of propagation of crack growth. The models for each ply configuration relate ply thickness and ply toughness to the corresponding in situ ply strength. Calculated results for several materials are shown to correlate well with experimental results.

Fracture Mechanics: With an Introduction to Micromechanics

Abstract: Elements of solid mechanics -- Classical failure hypotheses -- Micro and macro phenomena of fracture -- Linear fracture mechanics -- Elastic-plastic fracture mechanics -- Creep fracture -- Dynamic fracture mechanics -- Micromechanics and homogenization -- Damage mechanics -- Probabilistic fracture mechanics.

Stress intensity factor measurements from digital image correlation: post-processing and integrated approaches

Abstract: Digital image correlation is an appealing technique for studying crack propagation in brittle materials such as ceramics. A case study is discussed where the crack geometry, and the crack opening displacement are evaluated from image correlation by following two different measurement and identification routes. The displacement uncertainty can reach the nanometer range even though optical pictures are dealt with. The stress intensity factor is estimated with a 7% uncertainty in a complex loading set-up without having to resort to a numerical modelling of the experiment.

A generalized Paris' law for fatigue crack growth

Abstract: An extension of the celebrated Paris law for crack propagation is given to take into account some of the deviations from the power-law regime in a simple manner using the Wohler SN curve of the material, suggesting a more general ''unified law''. In particular, using recent proposals by the first author, the stress intensity factor K(a) is replaced with a suitable mean over a material/structural parameter length scale Da, the ''fracture quantum''. In practice, for a Griffith crack, this is seen to correspond to increasing the effective crack length of Da, similarly to the Dugdale strip-yield models. However, instead of including explicitly information on cyclic plastic yield, short-crack behavior, crack closure, and all other detailed information needed to eventually explain the SN curve of the material, we include directly the SN curve constants as material property. The idea comes as a natural extension of the recent successful proposals by the first author to the static failure and to the infinite life envelopes. Here, we suggest a dependence of this fracture ''quantum'' on the applied stress range level such that the correct convergence towards the Wohler-like regime is obtained. Hence, the final law includes both Wohler's and Paris' material constants, and can be seen as either a generalized Wohler's SN curve law in the presence of a crack or a generalized Paris' law for cracks of any size. r 2006 Elsevier Ltd. All rights reserved.

Dynamical fracture instabilities due to local hyperelasticity at crack tips

Abstract: As the speed of a crack propagating through a brittle material increases, a dynamical instability leads to an increased roughening of the fracture surface. Cracks moving at low speeds create atomically flat mirror-like surfaces; at higher speeds, rougher, less reflective ('mist') and finally very rough, irregularly faceted ('hackle') surfaces are formed. The behaviour is observed in many different brittle materials, but the underlying physical principles, though extensively debated, remain unresolved. Most existing theories of fracture assume a linear elastic stress-strain law. However, the relation between stress and strain in real solids is strongly nonlinear due to large deformations near a moving crack tip, a phenomenon referred to as hyperelasticity. Here we use massively parallel large-scale atomistic simulations--employing a simple atomistic material model that allows a systematic transition from linear elastic to strongly nonlinear behaviour--to show that hyperelasticity plays a governing role in the onset of the instability. We report a generalized model that describes the onset of instability as a competition between different mechanisms controlled by the local stress field and local energy flow near the crack tip. Our results indicate that such instabilities are intrinsic to dynamical fracture and they help to explain a range of controversial experimental and computational results.

Mixed mode brittle fracture in PMMA—An experimental study using SCB specimens

Abstract: A series of mixed mode I/II fracture tests is conducted on polymethylmethacrylate (PMMA) in the full range from pure mode I to pure mode II using a semi-circular bend (SCB) specimen containing an edge crack. The fracture load and the path of crack growth are obtained from experiments for various crack angles. It is shown that the conventional mixed mode I/II fracture criteria such as the maximum tangential stress (MTS) criterion overestimate the fracture strength of PMMA when the SCB specimen is used for fracture tests, particularly for mode II dominant loading conditions. However, improved predictions of fracture load are achieved when a generalized MTS criterion is employed. While the path of crack growth is straight for pure mode I, it deviates significantly from the angle of fracture initiation for pure mode II and mode II dominant loading conditions. It is shown that the path of crack growth predicted by the generalized MTS criterion is also in a good agreement with the observed fracture path in the fractured SCB samples.

Multiparadigm modeling of dynamical crack propagation in silicon using a reactive force field

Abstract: We report a study of dynamic cracking in a silicon single crystal in which the ReaxFF reactive force field is used for several thousand atoms near the crack tip, while more than 100 000 atoms are described with a nonreactive force field. ReaxFF is completely derived from quantum mechanical calculations of simple silicon systems without any empirical parameters. Our results reproduce experimental observations of fracture in silicon including changes in crack dynamics for different crack orientations.

Sub-surface mechanical damage distributions during grinding of fused silica

Abstract: The distribution and characteristics of surface cracking (i.e., sub-surface damage or SSD) formed during standard grinding processes have been measured on fused silica glass using a surface taper polishing technique. The measured SSD depth distributions are described by a single exponential followed by an asymptotic cutoff in depth. The observed surface cracks are characterized as near-surface lateral and deeper trailing indent type fractures (i.e., chatter marks). The length of the trailing indent is strongly correlated with a given grinding process. It is shown that only a small fraction of the abrasive particles are being mechanically loaded and causing fracture, and most likely it is the larger particles in the abrasive particle size distribution that bear the higher loads. The SSD depth increased with load and with a small amount of larger contaminant particles. Using a simple brittle fracture model for grinding, the SSD depth distribution has been related to the SSD length distribution to gain insight into ‘effective’ size distribution of particles participating in the fracture. Both the average crack length and the surface roughness were found to scale linearly with the maximum SSD depth. These relationships can serve as useful rules-of-thumb for non-destructively estimating SSD depth and for identifying the process that caused the SSD.

Molecular-dynamics simulation-based cohesive zone representation of intergranular fracture processes in aluminum

Abstract: A traction-displacement relationship that may be embedded into a cohesive zone model for microscale problems of intergranular fracture is extracted from atomistic molecular-dynamics simulations. A molecular-dynamics model for crack propagation under steady-state conditions is developed to analyze intergranular fracture along a flat 99 [1 1 0] symmetric tilt grain boundary in aluminum. Under hydrostatic tensile load, the simulation reveals asymmetric crack propagation in the two opposite directions along the grain boundary. In one direction, the crack propagates in a brittle manner by cleavage with very little or no dislocation emission, and in the other direction, the propagation is ductile through the mechanism of deformation twinning. This behavior is consistent with the Rice criterion for cleavage vs. dislocation blunting transition at the crack tip. The preference for twinning to dislocation slip is in agreement with the predictions of the Tadmor and Hai criterion. A comparison with finite element calculations shows that while the stress field around the brittle crack tip follows the expected elastic solution for the given boundary conditions of the model, the stress field around the twinning crack tip has a strong plastic contribution. Through the definition of a Cohesive-Zone-Volume-Element an atomistic analog to a continuum cohesive zone model element - the results from the molecular-dynamics simulation are recast to obtain an average continuum traction-displacement relationship to represent cohesive zone interaction along a characteristic length of the grain boundary interface for the cases of ductile and brittle decohesion. Keywords: Crack-tip plasticity; Cohesive zone model; Grain boundary decohesion; Intergranular fracture; Molecular-dynamics simulation

Effect of mechanical properties measured at room and elevated temperatures on the wear resistance of cutting tools with TiAlN and AlCrN coatings

Abstract: A comprehensive study of the mechanical properties of TiAlN and AlCrN coated cutting tools has been performed at room and elevated temperatures (up to 500 °C) using Micro Material's NanoTest Platform System. Micro-mechanical properties have been measured such as microhardness, elastic modulus, H/E ratio, microhardness dissipation parameter (MDP), critical load values ( L c1 —first crack event; L c2 —load of dramatic coating failure) during scratch testing; a scratch crack propagation resistance parameter, CPR s = L c1 ( L c2 − L c1 ) as well as nano-impact fracture resistance. Cutting tool life was studied under end milling conditions of the structural AISI 1040 steel. A correlation between CPR s was found with H/E ratio and MDP values. These parameters could be used to characterize the fracture toughness of the coatings. It was shown that mechanical characteristics such as H/E ratio, MDP and CPR s as well as nano-impact fracture resistance can be used to assess the resistance to adhesive-fatigue wear that is typical for end milling conditions. It was found that the microhardness of the coating and the H/E ratio reduces with rising temperature while the MDP value grows. The data obtained during quick laboratory nanohardness, nanoscratch as well as nano-impact fatigue testing can be used to rank the coatings studied and in some cases predict the relative life of a coated tool.

Simulation of Crack Propagation in Asphalt Concrete Using an Intrinsic Cohesive Zone Model

Abstract: This is a practical paper which consists of investigating fracture behavior in asphalt concrete using an intrinsic cohesive zone model (CZM). The separation and traction response along the cohesive zone ahead of a crack tip is governed by an exponential cohesive law specifically tailored to describe cracking in asphalt pavement materials by means of softening associated with the cohesive law. Finite-element implementation of the CZM is accomplished by means of a user subroutine using the user element capability of the ABAQUS software, which is verified by simulation of the double cantilever beam test and by comparison to closed-form solutions. The cohesive parameters of finite material strength and cohesive fracture energy are calibrated in conjunction with the single-edge notched beam [SE(B)] test. The CZM is then extended to simulate mixed-mode crack propagation in the SE(B) test. Cohesive elements are inserted over an area to allow cracks to propagate in any direction. It is shown that the simulated crack trajectory compares favorably with that of experimental results.

Development of the local approach to fracture over the past 25 years: Theory and applications

Abstract: This review paper is devoted to the local approach to fracture (LAF) for the prediction of the fracture toughness of structural steels. The LAF has been considerably developed over the past two decades, not only to provide a better understanding of the fracture behaviour of materials, in particular the failure micromechanisms, but also to deal with loading conditions which cannot easily be handled with the conventional linear elastic fracture mechanics and elastic-plastic fracture mechanics global approaches. The bases of this relatively newly developed methodology are first presented. Both ductile rupture and brittle cleavage fracture micromechanisms are considered. The ductile-to-brittle transition observed in ferritic steels is also briefly reviewed. Two types of LAF methods are presented: (i) those assuming that the material behaviour is not affected by damage (e.g. cleavage fracture), (ii) those using a coupling effect between damage and constitutive equations (e.g. ductile fracture). The micromechanisms of brittle and ductile fracture investigated in elementary volume elements are briefly presented. The emphasis is laid on cleavage fracture in ferritic steels. The role of second phase particles (carbides or inclusions) and grain boundaries is more thoroughly discussed. The distinction between nucleation and growth controlled fracture is made. Recent developments in the theory of cleavage fracture incorporating both the effect of stress state and that of plastic strain are presented. These theoretical results are applied to the crack tip situation to predict the fracture toughness. It is shown that the ductile-to-brittle transition curve can reasonably be well predicted using the LAF approach. Additional applications of the LAF approach methods are also shown, including: (i) the effect of loading rate and prestressing; (ii) the influence of residual stresses in welds; (iii) the mismatch effects in welds; (iv) the warm-prestressing effect. An attempt is also made to delineate research areas where large improvements should be made for a better understanding of the failure behaviour of structural materials.

Solvent control of crack dynamics in a reversible hydrogel

Abstract: The resistance to fracture of reversible biopolymer hydrogels is an important control factor of the cutting/slicing and eating characteristics of food gels It is also critical for their utilization in tissue engineering, for which mechanical protection of encapsulated components is needed Its dependence on loading rate and, recently, on the density and strength of cross-links has been investigated But no attention was paid so far to solvent nor to environment effects Here we report a systematic study of crack dynamics in gels of gelatin in water/glycerol mixtures We show on this model system that: (i) increasing solvent viscosity slows down cracks; (ii) soaking with solvent increases markedly gel fragility; (iii) tuning the viscosity of the (miscible) environmental liquid affects crack propagation via diffusive invasion of the crack tip vicinity The results point toward the fact that fracture occurs by viscoplastic chain pull-out This mechanism, as well as the related phenomenology, should be common to all reversibly cross-linked (physical) gels

Analytical Model for Corrosion-Induced Crack Width in Reinforced Concrete Structures

Abstract: Crack width is a parameter of the most practical significance for the design and assessment of reinforced concrete structures. Practical experience and observations suggest that corrosion-affected reinforced concrete structures are more prone to cracking than other forms of structural deterioration. Moreover, concrete cracking incurs considerable costs of repairs and inconvenience to the public due to interruptions. This gives rise to the need for a thorough investigation to achieve cost-effectiveness in maintaining the serviceability of concrete structures. This study attempts to derive an analytical model for corrosion-induced crack width based on the concept of smeared cracks. A merit of the derived model is that it is directly related to critical factors that affect the corrosion-induced concrete cracking. After verifying the derived model, a parametric study was undertaken to quantify the effect of these factors on cracking development. It was found that corrosion rate, as represented by corrosion current density icorr, is the most important single factor that affects both the time to surface cracking and the growth of crack width. It is concluded that the model derived in this paper can predict corrosion-induced crack width with reasonable accuracy.

Strength and sharp contact fracture of silicon

Abstract: The fracture strength of Si is considered in the context of yield and reliability of microelectronic and microelectromechanical (MEMS) devices. An overview of Si fracture, including the strength of Si wafers, dice and MEMS elements, highlights the importance of understanding sharp contact flaws, with their attendant residual stress fields, lateral cracks and strength-limiting half-penny cracks in advanced Si device manufacturing. Techniques using controlled indentation flaws, including measurements of hardness, crack lengths, crack propagation under applied stress, and inert and reactive strengths, are applied in an extensive new experimental study of intrinsic, n- and p-type {100} and {110} Si single crystals and polycrystalline Si, addressing many of the issues discussed in the overview. The new results are directly applicable in interpreting the strengths of ground or diced Si wafer surfaces and provide a foundation for studying the strengths of MEMS elements, for which the strength-controlling flaws are less well-defined. Although the indentation fracture behavior of Si is shown to be quite anisotropic, the extensive lateral cracking greatly affects crack lengths and strengths, obscuring the underlying single crystal fracture anisotropy. No effects of doping on fracture are observed. Strength decreases in water and air suggest that Si is susceptible to reactive attack by moisture, although the effect is mild and extremely rapid. Strength increases of indented components after buffered HF etching are shown to be due to reactive attack of the contact impression, leading to residual stress relief.