Bridging Stress Distribution Research Articles

In-situ damage mechanism investigation and a prediction model for delamination with fibre bridging in composites

Carbon-fibre reinforced composites are susceptible to delamination. Fibre bridging is an important shielding mechanism frequently observed in delamination. The presence of these bridging fibres can significantly increase interlaminar resistance, making it critical to represent this phenomenon for delamination characterization in composite laminates. To this end, in-situ SEM examinations were carried out to thoroughly explore damage mechanisms around delamination front as well as in bridging fibres. It was found that micro-cracks initiated at fibre–matrix interface can gradually develop and coalesce into micro-delaminations ahead of the main crack. The accumulation of these micro-delaminations can finally cause macro delamination propagation. The performance of bridging fibres can be summarized as three typical stages, i.e. bending, fibre–matrix peeling and final breakage with crack opening. Subsequently, theoretical discussions on bridging stress distribution were conducted in accordance with these bridging mechanism examinations, contributing to a new traction-separation constitutive to represent fibre bridging performance. A FEA prediction model was finally developed to characterize delamination behavior with fibre bridging. The simulation results can agree well with the experimental data in the entire delamination, demonstrating its effectiveness in fibre-bridged delamination representation. This study also demonstrated the importance of having in-depth understanding on fibre bridging mechanisms to appropriately represent bridging performance during delamination growth in composite laminates.

Investigation of analytical model of crack propagation under multi axial fatigue in fiber metal laminate

Mostly the aerospace and other applications parts during their service life are subjected to the multi axial fatigue with non-proportional loading. In this study, the fatigue crack growth in glass laminate aluminum reinforced epoxy subjected to special case of non-proportional multiaxial fatigue (cyclic tension with constant shear) has been investigated. New prediction analytical model used empirical Paris equation has been adopted. Crack-growth rate was in relation with the equivalent stress-intensity factor for mixed mode at the crack-tip. Bridging stress-intensity factor was superimposed with the far-field stress-intensity factors to evaluate the equivalent stress-intensity factor. Bridging stress distribution, crack opening contour, delamination shape and its growth have been estimated simultaneously to evaluate the bridging stress-intensity factor. The obtained results indicated that there was a considerable enhancement in the crack growth rate (193.8%), number of cycles required to full failure (192%) and other performance characteristic as compared with the monolithic aluminum. Numerical simulation by ABAQUS 2021 software has been implemented to verification of the analytical model. A significant convergence in behavior between the extracted results from both analytical model and numerical simulation with maximum deviation reach to 8.2%.

Fatigue Threshold R‐curves Predict Fatigue Endurance Strength for Self‐Reinforced Silicon Nitride

There is a need for methods that can help predict and avoid fatigue failures of silicon nitride ceramic components. The fatigue threshold R‐curve has been proposed as potential solution to this problem. In this study, the fatigue threshold R‐curve for small, semielliptical surface cracks was calculated for a silicon nitride ceramic using the published bridging stress distribution developed from fatigue threshold tests on macroscopic crack specimens. To test the accuracy of the endurance strengths predicted using the fatigue threshold R‐curve, fatigue tests were conducted using four‐point bend beams of silicon nitride containing semielliptical surface cracks introduced by Knoop indentation. The effectiveness of the methodology was verified; indeed, 77% of the beams tested at stress levels above the predicted endurance strength failed within 107 cycles and 0% of the beams tested below the predicted endurance strength failed within 107 cycles. Furthermore, using the bridging stress distribution, which is thought to be a material property, the need for prohibitively difficult fatigue threshold experiments on small surface cracks is avoided. Accordingly, this methodology is potentially quite practical for use in the engineering design of ceramic mechanical components.

A generalized solution to the crack bridging problem of fiber metal laminates

The slow crack growth and high residual strength of fiber metal laminates (FMLs) results from bridging, the transfer of loads from cracked metal layers to intact fiber layers that “bridge” the cracks over delaminations between the laminae. Understanding and improving the structural performance of FMLs therefore depends on characterizing the bridging phenomenon. Previously, mathematical models of bridging load transfer have been developed and verified for simplified circumstances:thin laminates with identical thicknesses and material composition through the laminate, identical crack lengths and delamination sizes, and simple tension loads. These models use a compatibility requirement at the delamination boundary to derive the bridging stress. This paper presents a generalized approach to solving the bridging problem that solves simultaneously for compatibility at every delamination boundary in the laminate, allowing the bridging load distribution to be derived for a laminate of arbitrary layup (different thicknesses and materials) with arbitrary damage (independent crack lengths and delamination sizes and shapes) and subject to arbitrary loading (any combination of applied tension and bending moment). The approach is evaluated by comparing its results to bridging stress distributions derived from finite element analysis. Good agreement was obtained for varied laminate and damage configurations, but some discrepancy exists in the presence of bending.

A direct comparison of non-destructive techniques for determining bridging stress distributions

Crack bridging is an important source of crack propagation resistance in many materials and the bridging stress distribution as a function of crack opening displacement is widely believed to represent a true material property uninfluenced by sample geometry, loading conditions, and other extrinsic factors. Accordingly, accurate measurement of the bridging stress distribution is needed and many non-destructive methods have been developed. However, there are many challenges to accurately determining bridging stresses. A comparison of bridging stresses measured using R-curve, crack opening displacement (COD), and spectroscopy methods has been made using two bridging ceramics, Y2O3 and MgO doped Si3N4 and 99.5% pure Al2O3. The COD method is surface sensitive and gives a lower peak bridging stress compared to the R-curve technique which samples through the entire material thickness. This is attributed to a more compliant near surface bridging zone. Conversely, when R-curves rise steeply over the first few micrometers of growth from a notch, an effect of negative T-stress is expected to raise the R-curve determined peak bridging stress. Spectroscopy methods were only found to yield reliable bridging stress results if a reasonable through thickness volume of material is sampled. It was found that 2.5% of the specimen thickness achieved using fluorescence spectroscopy appears adequate for Al2O3 while 0.1–0.2% of the sample thickness achieved using Raman spectroscopy for Si3N4 appears inadequate. Overall, it is concluded that in the absence of T-stresses a bridging distribution can be determined that is a true material property. Also, a new method is proposed for determining the bridging stresses of fatigue cracks from (1) the bridging stress distribution for monotonically loaded cracks and (2) experimental fatigue data.

Fatigue threshold R-curves predict small crack fatigue behavior of bridging toughened materials

Small crack fatigue is a widely recognized problem in the fatigue of materials; however, there has been limited progress in developing methods to predict small crack fatigue behavior. In this paper small crack effects due to crack bridging are addressed. A fatigue threshold R-curve was measured for a 99.5% pure polycrystalline alumina using standard compact tension specimens and was used (i) to determine the bridging stress profile for the material and (ii) to make fatigue endurance strength predictions for realistic semi-elliptical surface cracks. Furthermore, it has been shown that the fatigue threshold R-curve can equivalently be determined by measuring the bridging stress distribution, in this case using fluorescence spectroscopy, using only a long crack compact tension specimen without the need for difficult small crack experiments. It is expected that this method will be applicable to a wide range of bridging toughened materials, including composites, toughened ceramics, intermetallics, and multi-phase materials.

Mechanisms of toughening in silicon nitrides: The roles of crack bridging and microstructure

Crack-bridging mechanisms can provide substantial increases in toughness coupled with strength in ceramics. Herein, we describe the various bridging mechanisms, their toughening contributions and how they are affected by microstructure in silicon nitride ceramics, which are a classic example where both high strength and toughness are achieved. Crack growth resistance curves ( R-curves) for seven different silicon nitrides doped with various metal oxides and with different microstructures were measured, and bridging stress distributions were calculated for each. Based on an analysis of those results combined with results of the relative interfacial toughness of two of the ceramics, a new mechanistic theory for the evolution of the R-curve is proposed. The initial steep rise in toughness is attributed to the formation of elastic bridges that experience no debonding. This mechanism has not previously been recognized in the literature and the high strength of these materials (up to 1 GPa) is here attributed primarily to that mechanism. As those bridges begin to fracture and the mechanism becomes saturated, a change in the R-curve slope is observed and the more traditional mechanisms of partially debonded elastic and fully debonded frictional bridges dominate the continuing rise in toughness. Furthermore, the saturation of each mechanism is associated with a change in slope of the R-curve. The results of this study provide a fundamental insight into how to optimize silicon nitride microstructures for high strength and toughness.

Influences of Crack Face Bridging Stress and Microstructure on Fracture Toughness of Toughened Alumina Ceramics

Three types of polycrystalline alumina, one pressureless and two hot press sintered Al2O3, were used to examine the effects of the characteristics of microstructure and crack face bridging on fracture toughness. The crack opening displacements and microstructures along the pop-in crack of single edge precracked beam (SEPB) specimens were observed in situ at a constant applied stress intensity factor by scanning electron microscopy (SEM). The bridging stress distribution could be determined from the measured crack opening displacement by three-dimensional finite element analysis, and then the stress intensity factor and stress shielding effect at the crack tip could also be determined. Intergranular microcracks of toughened Al2O3 were deflected by a complicated microstructure, and crack closure due to bridging grains was observed near the crack tip. Bridging stress of Al2O3 was compressive perpendicular to the crack face and was distributed behind the crack tip. The maximum bridging stress of two hot press sintered Al2O3 was about twice as large as that of pressureless sintered Al2O3. The fracture toughness of hot press sintered Al2O3 was, therefore, higher than that of pressureless sintered Al2O3, because the total amount of bridging stress and stress shielding effect increased with increasing magnitude of microcrack deflection and the number of interlocking grains.

763 高じん性アルミナのき裂面架橋応力分布評価(OS7-5 非線形力学,OS7 先進材料および構造の力学特性評価)

763 高じん性アルミナのき裂面架橋応力分布評価(OS7-5 非線形力学,OS7 先進材料および構造の力学特性評価)

Application of Mechanoluminescence for the Dynamic Visualization of an Alumina Fracture

The propagation of cracks was quantitatively analyzed in Al2O3 ceramic using the mechanoluminescence (ML) of SrAl2O4:Eu,Dy. The bridging zones behind the crack tip were clearly detected in the crack path of Al2O3 within a realistic time frame. The magnitudes and shapes of the bridging stress distributions changed with the advancing cracks. They continued to change with the change in the applied load even after the cessation of crack propagation. Effective toughening then commenced, and the applied stress intensity factors dramatically increased up to ∼50 MPa√m . The expected KTip values based on the instantaneous bridging stress distributions obtained from the ML observations deviated greatly from those obtained from the measurement using the conventional crack tip lengths; rather, they support the results obtained when bridging tips were used in the quasidynamic crack propagations.

Quasi-dynamic visualization of crack propagation and bridging evolution in Si3N4 and SiC ceramics by mechano-luminescence

The propagations of macro-scale cracks were visualized in Si3N4 and SiC ceramics using a mechano-luminescence (ML) of SrAl2O4:Eu,Dy. The bridging zones behind the crack tip were also clearly detected in the crack path within realistic time frames. The ML made it possible to detect cracks propagating within a speed range of 200 m/s to 250 m/s, thereby realizing so-called quasi-dynamic R-curves. The magnitudes and shapes of the bridging stress distributions were found to change with the advancing cracks, continuing to change as the applied load changes, even after the cessation of crack propagation. The effective toughening then commenced and the applied stress intensity factors increased dramatically up to ∼120 MPa√m in Si3N4 and 150 MPa√m in SiC. The KTip values expected on the basis of the instantaneous bridging stress distributions obtained from ML observations deviated greatly from those measured using the conventional crack tip lengths; rather, the values support the results obtained by using bridging tips in quasi-dynamic crack propagations.

Detection of Crack Propagation in Alumina Using SrAl<sub>2</sub>O<sub>4</sub>:(Eu,Dy) Luminescent Paint

Using a mechano-luminescent (ML) paint enabling the visualization of fast propagating crack as well as bridging stress distribution under a conventional loading condition, this paper presents a catastrophic fracture mechanism in association with the crack wake bridging in alumina ceramics. The bridging stress distribution evolves in its magnitude and shape as crack advances and keeps changing as load changes even for a stationary crack. An instantaneous stress intensity factor skyrocketed extraordinarily up to 120 MPa√m, which is due to the well-known effect of specimen dimension and the accurate location of real crack tip by the ML technique.

Visualization of fractures in alumina ceramics by mechanoluminescence

The use of a mechanoluminescent (ML) paint enables a propagating crack and bridging stress distribution to be visualized. This technique was used to examine the mechanism of fracture in alumina ceramics. The mechanism appears to be inconsistent with currently accepted R-curve concepts. The magnitude and shape of the bridging stress distribution changes with the advancing crack. It continues to change as the applied load changes, even after the cessation of crack propagation. The measured R-curve increased dramatically up to 120 MPa m . ML technology provides not only a versatile tool for the study of fracture mechanism, but also has the potential for use in the low-cost safety diagnosis of structural components or the visualization of microelectromechanical systems operations.

Effects of fibre debonding and sliding on the fracture behaviour of fibre-reinforced composites

Abstract The effects of interfacial debonding and sliding on fracture characterisation of unidirectional fibre-reinforced composites are studied numerically under plane strain and small-scale bridging conditions. To account for the importance of fiber architecture, the fracture process zone (FPZ) characterised by discrete embedded reinforcement and cracking matrix, is of discontinuous bridging stresses. A bi-linear bridging law is incorporated in the finite element (FE) model to assess the effect of interfacial debonding and sliding. A linearly decreasing traction–separation law describes matrix cracking in brittle matrix. Transversely isotropic, orthotropic elastic constitutive relation is used for the effective properties of bulk brittle-matrix composites outside the FPZ. A boundary-layer formulation is imposed on the remote boundary based on the elastic solutions for mode I crack problems. Crack advance and fibre breakage are direct consequences of the constitutive modelling without any ad hoc crack growth criteria. The proposed FE model can eliminates unreal singular stresses ahead of the matrix crack. Fracture resistance (R) curves are obtained for a range of interfacial properties, as well as stress and bridging stress distributions. It is found that the toughness can be enhanced by modification of interfacial properties. Numerical results also show that fibre fracture results in a significant reduction of the steady-state toughness and relief of high stress concentration. However, strongly bonded interface implies a high interfacial strength, but a low toughness due to a low fibre strength.

Mechanistic aspects of fracture and R-curve behavior in human cortical bone

An understanding of the evolution of toughness is essential for the mechanistic interpretation of the fracture of cortical bone. In the present study, in vitro fracture experiments were conducted on human cortical bone in order to identify and quantitatively assess the salient toughening mechanisms. The fracture toughness was found to rise linearly with crack extension (i.e., rising resistance- or R-curve behavior) with a mean crack-initiation toughness, K 0 of ∼2 MPa√m for crack growth in the proximal–distal direction. Uncracked ligament bridging, which was observed in the wake of the crack, was identified as the dominant toughening mechanism responsible for the observed R-curve behavior. The extent and nature of the bridging zone was examined quantitatively using multi-cutting compliance experiments in order to assess the bridging zone length and estimate the bridging stress distribution. Additionally, time-dependent cracking behavior was observed at stress intensities well below those required for overload fracture; specifically, slow crack growth occurred at growth rates of ∼2×10 −9 m/s at stress intensities ∼35% below the crack-initiation toughness. In an attempt to measure slower growth rates, it was found that the behavior switched to a regime dominated by time-dependent crack blunting, similar to that reported for dentin; however, such blunting was apparent over much slower time scales in bone, which permitted subcritical crack growth to readily take place at higher stress intensities.

Mechanistic Aspects of Fracture of Human Cortical Bone

AbstractThere has been growing interest of late in the fracture properties of human bone. As understanding such properties in the context of the hierarchical microstructure of bone is of obvious importance, this study addresses the evolution of the in vitro fracture toughness with crack extension (Resistance-curve behavior) in terms of the salient mechanisms involved. Fracture-mechanics based measurements were performed on compact-tension specimens hydrated in Hanks' Balanced Salt Solution using cortical bone from mid-diaphyses of 34-41 year-old human humeri. Post-test observations of the crack path were made by optical microscopy and three-dimensional X-ray computed tomography. The fracture toughness was found to rise linearly with crack extension with a mean crack-initiation toughness of Ko ∼ 2.0 MPa√m for crack growth in the proximal-distal direction. The increasing cracking resistance had its origins in several toughening mechanisms, most notably crack bridging by uncracked ligaments. Uncracked-ligament bridging, which was observed by tomography in the wake of the crack, was identified as the dominant toughening mechanism responsible for the observed Rcurve behavior through compliance-based experiments. The extent and nature of the bridging zone was examined quantitatively using multi-cutting compliance experiments in order to assess the bridging stress distribution. The results obtained in this study provide an improved understanding of the mechanisms associated with the failure of cortical bone, and as such are of importance from the perspective of developing a realistic framework for fracture risk assessment, and for determining how the increasing propensity for fracture with age can be prevented.

Modelling of R-curve behaviour in ceramic–metal laminates

In materials that display R-curve behaviour, the magnitude of the bridging stress is dependent on the local crack opening. Therefore, the bridging stress distribution and consequently, the toughness can be quite different for different crack geometries and crack lengths, even if the same bridging law is applied. In the present study, using the exact stress–displacement function ( σ( u)) of the constrained metal layer and a weight-function-based approach, it was possible to obtain the crack opening profile ( u( x)), and hence the bridging stress distribution along the bridging zone. The calculated displacement profiles using the weight function were checked by comparison with that obtained using the Finite Element Method at different crack sizes. Predicted fracture toughness resistance curves were compared to experimental results for different ceramic–metal combinations. The effect of different properties of the bridging layer (thickness, ductility, strength and debonding) on the predicted R-curve has been studied by their effect on the bridging traction-displacement relationship.

R-curve behavior of alumina toughened with molybdenum and zirconia particles

Alumina matrix was added with metal molybdenum and different amounts of zirconia's particles. R-curves were measured during stable crack propagation and a piezo-spectroscopic technique has been used to assess the bridging stresses developed along the crack wake at the critical condition for crack propagation. The theoretical R-curves calculated from the average (microscopic) bridging stress distribution obtained by in situ Raman spectroscopy were in good agreement with the experimental data. If the molybdenum content is kept constant but the ZrO 2 amount is increased, the toughening due to t- m transformation increases, but at the same time the metal/ceramic interface is weakened by the presence of zirconia and the toughening due to metal particles bridging decreases. As a result of that, the presence of zirconia has only a limited beneficial influence on the overall toughness. The overall composite toughness is due to transformation and bridging toughening mechanisms, however, the two mechanisms do not have synergistic effects and crack bridging by molybdenum particles appears to be the dominant toughening mechanism.

Inverse Analysis to Determine Crack Bridging Stress in Fiber Composites

This paper develops a method to determine “bridging law” for continuously aligned fiber composites to understand damage mechanisms from a maintenance engineering point of view. Fracture mechanics approach has been employed to form the integral equation for mathematical simulation of embedded straight cracks and single edge cracks in specimens of infinite or finite width under tensile and bending stresses. Closing pressure was assumed between the crack surfaces due to continuous fibers or aggregates which remain connected to both the crack surfaces. Inverse analysis is performed on crack opening displacement (COD) data to get magnitude and distribution of bridging stresses for fiber composites. Synthetic data were created by forward analysis for certain crack configurations to get exact COD data from a theoretical point of view. To simulate practical situations, data were made noisy by inserting noise of known levels. Exact bridging stress distributions were retrieved by the inverse analysis up to certain level of noisy data which establishes applicability of the method developed here.

Raman Microprobe Evaluation of Bridging Stresses in Highly Anisotropic Silicon Nitride

The microscopic bridging stress distribution developed behind the crack tip of a highly anisotropic silicon nitride has been measured along the crack profile using Raman microprobe spectroscopy with a micrometer spatial resolution. The near‐tip rising R‐curve behavior and the crack‐opening displacement (COD) profile of the material were also determined and discussed in comparison with the Raman microstress data. A comparison with the fracture behavior of a previously investigated silicon nitride material with a three‐dimensional random microstructure is also proposed. According to this set of micro/macroscopic fracture characterizations, a self‐consistent view of toughening behavior in silicon nitride ceramics is obtained, and the role on toughness of anisotropically oriented acicular grains clarified. In agreement with previous studies, it is confirmed that crack‐face bridging is the most effective mechanism for toughening silicon nitride ceramics.