Adherence of elastomers: Fracture mechanics aspects

Application of fracture mechanics concepts to adherence of elastic and viscoelastic solids is examined. It is shown that the Dugdale-Barenblatt model could be applied both for explaining the transition from Johnson-Kendall-Roberts to Deryagin-Muller-Toporov solution in adherence of spheres, and for liquid bridges. The problem of the threshold energy release rate G₀ for elastomers is considered. It is proposed to add to the viscoelastic losses a supplementary friction term when polymeric chains strongly held at the interface by primary bonds are pulled out.     

高分子材料断裂力学评价方法研究进展

简要介绍了线弹性断裂力学、弹塑性断裂力学和基本断裂功这3种方法的理论背景和前提假设、材料参数的试验测试方法和计算过程、试样预制裂纹对测试结果的影响以及近些年在高分子材料上的应用研究进展,并对3种研究方法的应用范围和特点,具体实用效果进行了对比分析。     

Controlled Precracking of Fracture Mechanics Specimens Using Contact Stresses

A simple method is proposed for introducing precracks into thin-plate fracture mechanics specimens, i.e., compact-tension and double-cantilever-beam specimens, using standard testing equipment and without performing complicated machining operations on the specimens. The surface of the specimen is first scored to a known length, using a scribe, and the specimen is then compressed between polymer blocks. Mismatch between the elastic properties of the polymer and the specimen results in an in-plane tensile stress in the vicinity of the scratch that causes a crack to initiate from the scratch and propagate through the specimen thickness. Provided that certain conditions are met, the crack arrests without significant growth beyond the initial scratch length. The result is a straight, through-thickness precrack of controllable length. Fracture toughness measurements made on glass specimens precracked using the proposed method are in good agreement with literature values for this material.     

Fracture Mechanics of Titanium/Bioactive Glass-Ceramic Particulate Composites

Composite bioactive glass-ceramics reinforced with 30 vol% Ti particles were produced by warm-forging and in situ crystallization. The bend strength of the composite was 87 ± 7 MPa. A fracture mechanical study in air and Ringer's bioactive solution determined crack velocity vs stress intensity factor and the effect of stressing rate on the bend strength. Time to failure of 10 years is predicted for the composite loaded at 10 MPa in Ringer's solution or 50 MPa in air. A disappointing fatigue performance of the relatively tough metal/ceramic composite illustrates that satisfactory short-time fracture resistance does not guarantee lifetime under fatigue conditions (long-term fracture resistance).     

Elastic Fracture Mechanics of the Peel-Test Geometry

The results of a linear-elastic analysis to determine the phase angle at the tip of an interface crack in the peel test are presented in this paper. The phase angle is fairly insensitive to the peel angle and, when the film and substrate have identical elastic properties, the mode-I and mode-II components of the crack-tip stress field are approximately equal. The phase angle has some dependence on both the elastic mismatch and the applied force; it is very sensitive to any residual strains in the film.     

Elastic Fracture Mechanics of the Peel-Test Geometry

The results of a linear-elastic analysis to determine the phase angle at the tip of an interface crack in the peel test are presented in this paper. The phase angle is fairly insensitive to the peel angle and, when the film and substrate have identical elastic properties, the mode-I and mode-II components of the crack-tip stress field are approximately equal. The phase angle has some dependence on both the elastic mismatch and the applied force; it is very sensitive to any residual strains in the film.     

Toughness Optimization of SBR Elastomers – Use of Fracture Mechanics Methods for Characterization

Elastomer materials are used in a wide application range and subjected to different loading from which failure of the material results. Because this failure is caused by initiation and propagation of cracks, the application of fracture mechanics methods for the assessment of the material is obvious. A short summary of the methods of technical fracture mechanics including possibilities of determination of crack resistance curves is given. Vulcanizates on the basis of SBR 1500 with various sulfur and carbon black contents were investigated. For describing the crack initiation and crack propagation behavior, several fracture mechanics examination methods were applied. Tear‐analyzer results were used to assess the crack propagation behavior under fatigue‐like loading conditions. Furthermore, for the characterization of the crack resistance of the materials under impact‐like loading conditions, instrumented tensile‐impact tests were performed. To obtain information about the initiation and propagation of a stable crack, quasi‐static fracture mechanics tests were applied. The results of the several tests are discussed in dependence on sulfur and carbon black contents. We found a non‐monotonous behavior of the toughness as a function of carbon black loading. An explanation is given in connection with a percolation‐like transition in filler morphology on larger length scales.

Schematic crack propagation curve for characterizing the fatigue behavior of the vulcanizates recorded in a TFA test.     

Investigation of Thermal Shock in a High-Temperature Refractory Ceramic: A Fracture Mechanics Approach

The results of a study on the thermal shock behavior of a high-temperature refractory ceramic that is used as a furnace liner in the melting of steels are presented in this paper. The experimental studies show that thermal shock damage initiates by edge cracking after the first shock cycle. Subsequent subcritical crack growth occurs by the incremental extension of dominant cracks until catastrophic failure occurs. The observations of the crack profiles also reveal the formation of viscoelastic bridges that promote crack-tip shielding/toughening via crack bridging. Following a brief discussion of the respective mechanisms of fracture and thermal shock damage at different temperatures and temperature ranges, the implications of the results are discussed for refractory ceramics that are toughened by viscoelastic crack bridging.     

Effect of Lateral Cracks on Fracture Toughness Determined by the Surface-Crack-in-Flexure Method

The surface-crack-in-flexure (SCF) method uses a Knoop indenter to create small, semielliptical surface precracks in beam specimens. Lateral cracks may interfere with the primary median crack and cause errors of up to 10% in determination of fracture toughness, particularly for materials for which the fracture toughness is ∼3 MPa·m^1/2 or less. Although the residual-stress-damage zone is ground or polished away by hand by removing 4.5–5 times the indentation depth, this amount may not be sufficient to completely remove the lateral cracks in low-fracture-toughness materials. A series of tests were conducted on sintered alpha silicon carbide with different amounts of material removed after indentation. Once the lateral cracks were fully removed, the SCF results concurred with single-edged-precracked-beam and chevron-notched-beam data collected in accordance with ASTM Designation C1421. A simple remedy for the SCF method is to examine the outer ground surface for remnants of lateral cracks before fracture and to remove more material if necessary.     

Adherence and Rolling Kinetics of a Rigid Cylinder in Contact with a Natural Rubber Surface

Equilibrium conditions of a rigid cylinder in contact with the flat and smooth surface of a natural rubber sample are studied using concepts of fracture mechanics, such as the strain energy release rate or the stress intensity factor. It is shown that an equilibrium contact area exists if the applied force per unit axial length is greater than a negative critical value, closely related to the cylinder radius and mechanical and superficial properties of the elastic solid. Due to the intervention of molecular attraction forces, of van der Waals type, a light cylinder rolls under an inclined rubber surface and it is displayed that the rolling speed is the same when the cylinder rolls upon the same inclined surface. It has been verified that if a flat rubber substrate, with an adequate length, is rotated at constant angular velocity, a steel cylinder rolls alternately upon and under the surface, unceasingly without falling down.     

Non Linear Fracture Mechanics for Adhesive Lap Joints

The Rice Cherepanov J is calculated for a lap joint in pure shear. By choosing as a condition for fracture a critical value J_c of this quantity the fracture load of the joint is calculated for linear elastic, perfectly plastic and linear hardening behavior of the adhesive. Comparisons are given with experiments with various adhesives and overlap lengths.     

Fracture Mechanics of High-Toughness Magnesia-Partially-Stabilized Zirconia

Crack growth resistance in MgO-partially-stabilized ZrO₂ (Mg-PSZ) has been studied using notched double-cantilever beams (DCB's). High-toughness Mg-PSZ exhibited nonlinear mechanical behavior in the form of residual displacements, related to the transformation of tetragonal ( t ) ZrO₂ precipitates to monoclinic ( m ) symmetry. The influence of this residual displacement on crack resistance behavior (" R -curve" behavior) was analyzed using several different fracture mechanics approaches. Specifically, the "global" resistance W _R (Δ a ), a J -integral type parameter W _J (Δ a ), were determined as a function of crack extension (Δ a ). Some of these parameters displayed a geometry dependence; their form depended on the initial notch depth and the size of the unbroken ligament. The early stages of crack growth were best described by W _J (δ a ). The residual strains building up in the wake during crack growth and their effect on specimen displacement made the W _R curves (and to some extent the W _J curves) dependent on the ratio between initial notch depth and crack extension. The only curves independent of geometry were the G (δ a ) curves, but only in a restricted range of geometry. However, the material resistance of Mg-PSZ is clearly under-estimated with such a linear elastic approach.     

A Comparison of Several Fracture Mechanics Methods for Measuring Interfacial Toughness with Microbond Tests

Several stress analysis methods were used to find the energy release rate for initiation of an interfacial crack in a microbond specimen. First, we used a recently-derived variational mechanics analysis of the stresses in a microbond specimen. Previous studies for analysis of crack growth have used shear-lag methods. For a second analysis, we present a new, and more complete, shear-lag analysis of the microbond specimen. Third, we consider some previously-published theories. For each of the stress analyses, the calculated energy release rate was used to predict the debonding stress as a function of the droplet length. The predictions were compared with two experimental results. Our new analyses that include residual thermal stresses were found to be the best. It was further observed that some of the terms in the analysis are negligible. The remaining terms provide a simple tool for doing a fracture mechanics analysis of microbond experiments.     

The Fatigue and Durability Behaviour of Automotive Adhesives. Part I: Fracture Mechanics Tests

A fracture mechanics approach has been successfully used to examine the cyclic fatigue behaviour of adhesively-bonded joints, which consisted of aluminium-alloy or electro-galvanised (EG) steel substrates bonded using toughened-epoxy structural paste-adhesives. The adhesive systems are typical of those being considered for use, or in use, for bonding load-bearing components in the automobile industry. The results were plotted in the form of the rate of crack growth per cycle, da/dN, versus the maximum strain-energy release rate, G_max, applied in the fatigue cycle, using logarithmic axes. Of particular interest was the presence of a threshold value of the strain-energy release rate, G_th, applied in the fatigue cycle, below which fatigue crack growth was not observed to occur. The cyclic fatigue tests conducted in a relatively dry environment of 23°C, and 55%; RH were shown to cause crack propagation at far lower values of G_max compared with the value of the adhesive fracture energies, G_c, which were determined from monotonically-loaded fracture tests. Cyclic fatigue tests were also conducted in a “wet” environment, namely immersion in distilled water at 28 C. The “wet” fatigue tests clearly revealed the further significant effect an aggressive, hostile environment may have upon the mechanical performance of adhesive joints, and highlighted the important influence that the surface pretreatment, used for the substrates prior to bonding, has upon joint durability. The development and standardisation of “wet” fatigue tests may provide the basis for a very effective accelerated-ageing test.     

Continuum and Fracture Mechanical Studies of Contaminated Bonding Surfaces

The importance of fracture mechanics testing of contaminated bonding surfaces is discussed. The sensitivity of adhesive bond systems to contamination may increase dramatically when macroscopic cracks are present. A bond system is shown to retain a significant level of tensile adhesion strength at relatively high levels of contamination, yet have near zero mode I fracture toughness at very low levels of the same contaminant. Silane adhesion promoter is shown to reduce greatly the system fracture toughness sensitivity to contamination, especially at lower levels of contamination.     

Continuum and Fracture Mechanical Studies of Contaminated Bonding Surfaces

The importance of fracture mechanics testing of contaminated bonding surfaces is discussed. The sensitivity of adhesive bond systems to contamination may increase dramatically when macroscopic cracks are present. A bond system is shown to retain a significant level of tensile adhesion strength at relatively high levels of contamination, yet have near zero mode I fracture toughness at very low levels of the same contaminant. Silane adhesion promoter is shown to reduce greatly the system fracture toughness sensitivity to contamination, especially at lower levels of contamination.     

Steady-State Mechanics of Delamination Cracking in Laminated Ceramic-Matrix Composites

A fracture mechanics delamination cracking model has been developed for brittle-matrix composite laminates. The near-tip mechanics is discussed in the context of material orthotropy and composite material inhomogeneities. A fracture mechanics framework based on the near-tip energy release rate and the associated phase angle Ψ has been adopted. In the case of steady-state delamination cracking in a prenotched cross-ply symmetric laminated beam, analytical expressions for the steady-state energy release rate, _ss, have been obtained for the combined applied loading of an axial force and a bending moment. Parameter studies assessing the effects on _ss of load coupling, crack location, and lamination morphology which includes the total number of layers, layer thickness, and material properties are presented. Thus, composite homogenization criteria with respect to the total number of layers placed along the beam height can be obtained for a wide range of material selection. The associated phase angle Ψ at the delamination crack tip is discussed in the context of existing solutions. The analysis has been developed based on a theory for structural laminates. The delamination model can be used in conjunction with experimental data obtained from model geometries to extract the mixed-mode transverse composite fracture toughness. Thus, conditions for stable delamination crack growth can be established and design criteria based on toughness for composite laminates and composite fasteners can be obtained.     

Time‐ and Temperature‐Dependent Fracture Mechanics of Polymers: General Aspects at Monotonic Quasi‐Static and Impact Loading Conditions

Well‐defined correlations exist between the maxima in mechanical loss factor and the local maxima in temperature‐ or loading‐speed‐dependent fracture toughness. The non‐linear viscoelastic fracture processes and small‐strain deformations are characterised by the same Arrhenius‐type activation enthalpies. The local increase in toughness is linearly correlated with the relaxation strength of molecular relaxation processes. Stable crack propagation can be understood as a three‐phase process resulting in steady‐state stable crack growth. The normalised steady‐state crack‐tip‐opening displacement is independent of matrix material, temperature and loading speed.

     

PBX断裂力学行为研究进展

从常用实验方法、细观断裂模式、宏观断裂力学以及动态断裂方面,概述了近年来国内外关于PBX断裂力学行为的研究状况;介绍了PBX宏观和细观断裂特征及表征手段;阐述了细观结构、力学特性、温度和加载率对PBX断裂行为的影响。指出应开展PBX细观微裂纹萌生和扩展、宏观起裂机理研究,及动态加载下PBX裂纹扩展行为研究,建立适合PBX材料特性的复合型断裂准则。附参考文献51篇。     

JKR-DMT transition in the presence of a liquid meniscus

In a previous paper [J. Colloid Interface Sci. 150, 243 (1992)], one of the authors (D.M.) has shown how, for the contact of elastic spheres, fracture mechanics with a Dugdale model of adhesion forces can lead to a general theory with the Johnson-Kendall-Roberts (JKR) and Derjaguin-Muller-Toporov (DMT) theories as limiting cases. The main equations are briefly recalled and the theory is applied to the case of a liquid meniscus around the contact. It is shown that the results are similar to those of Fogden and White [J. Colloid Interface Sci. 138, 414 (1990)]. Experiments with a surface force apparatus are described showing this transition in the presence of a liquid meniscus. The measured profiles are in good agreement with the theory.