Cohesive fracture modeling of crack growth in thick-section composites

This paper presents a combined method for modeling the mode-I and II crack growth behavior in thick-section fiber reinforced polymeric composites having a nonlinear material response. The experimental part of this study includes crack growth tests of a thick composite material system manufactured using the pultrusion process. It consists of alternating layers of E-glass unidirectional roving and continuous filament mats in a polymeric matrix. Integrated micromechanical and cohesive finite element (FE) models are used to simulate the crack growth response in eccentrically loaded single-edge-notch, (tension), ESE(T) and notched butterfly specimens. Micromechanical constitutive models for the mat and the roving layers are used to generate the effective nonlinear material behavior from the in situ fiber and matrix responses. The validity of the numerical modeling approach before the onset of crack growth is investigated using an infrared thermal method. Cohesive FE models are calibrated and used to simulate the complete crack growth behavior for different crack configurations. The proposed integrated framework of multi-scale material models with cohesive fracture models is shown to be an effective method for predicting the structural and material responses including failure load and crack growth in thick-section fiber reinforced polymeric composites.     

Eine neue Methode zur Festigkeits- und Zähigkeitsbestimmung von dünnen Schichten

A New Method of Determining Strength and Fracture Toughness of Thin Films A method is presented for measuring strength and fracture toughness of thin films. The basic idea of this method is to use a compact steel specimen as a substrate, which is deeply precracked by means of fatigue loading prior to the coating process. Under bend loading of this composite crack opening occurs accompanied by straining the free-standing thin film which bridges the crack. Film rupture firstly occurs at the front face of the specimen followed by crack growth on both sides. The film properties can be derived by eliminating the substrate effect through determining the difference between the two load-displacement curves corresponding to the intact and the damaged film, respectively. The strength of the film can be calculated from the load difference at film rupture at the front face of the composite. The fracture toughness is evaluated from load and compliance change during successive crack growth on both sides of the specimen. First results on PACVD TiN-films are presented and compared with available bulk data, thus demonstrating the applicability of the proposed method.     

Chevronproben zur näherungsweisen Bestimmung der Bruchzähigkeit

Chevron Specimen for the Estimation of Fracture Toughness Fracture toughness is a material property which is presently used in many industrial areas, either as material selection criteria or as material quality requirement. In some areas, nuclear power plants and aerospace, it is also a design parameter for design against catastrophic failures. Determination of the fracture toughness in accordance with ASTM E 399 is relatively elaborate. Depending on the material concerned, a certain minimum material cross section is required to obtain the necessary size of the specimen. Many semi-finished product forms of the different materials can not be tested for fracture toughness due to the specimen size requirements. For these reasons, alternative test methods were sought of which testing of chevron-notched specimens is one method. In the work to be presented, the test method to determine fracture toughness via chevron-notched specimens is briefly described. The most frequently used chevron-notched specimens are shown together with loading grips to be used in conjunctions with universal testing machines. Certain effects associated with some of the chevronnotched specimens are pointed out which result in a large difference between the fracture toughness determined in accordance with ASTM E 399 and that obtained via chevron-notched specimens. The aim of our research effort is to develop a chevron-notched specimen geometry which furnishes fracture toughness values compatible with K_Ic values without complicating the test method. Such a chevronnotched specimen is presented and the fracture toughness values obtained from these specimens of 7475-T 7351 and different Ti-alloys are compared to the K_Ic values obtained in accordance with ASTM E 399 for the same materials.     

Partially stiffened elastic half-plane with an edge crack

A technique, using the Brazilian disk specimen, for measuring the fracture toughness of unidirectional fiber-reinforced composites, over the entire range of crack-tip mode mixities, was developed. The fracture toughness of a graphite/epoxy fiber-reinforced composite was measured, under both mode-I and mode-II loading conditions. We found that for certain material orientations the mode-II fracture toughness is substantially higher than the mode-I toughness. The complete dependence of the fracture toughness on the crack-tip mixity was determined for particular material orientations and the phenomenological fracture toughness curves were constructed. Using the Brazilian disk specimen, together with a hydraulic testing machine, the fracture toughness of the composite under moderate loading rates was measured. We observed that the mode-I fracture toughness was not sensitive to the loading rate at the crack tip, K, while the mode-II ‘dynamic’ fracture toughness increased approximately 50 percent over the quasi-static fracture toughness. A qualitative explanation of the dependency of fracture toughness on crack-tip loading rate is discussed. Finally, a mechanical fracture criterion, at the microscopic level, which governs the crack initiation under mixed-mode loading conditions is presented; these theoretical predictions closely follow the trend of experimental measurements. This revised version was published online in August 2006 with corrections to the Cover Date.     

Determination of dynamic fracture parameters using a semi-circular bend technique in split Hopkinson pressure bar testing

Fracture initiation toughness, fracture energy, fracture propagation toughness, and fracture velocity are key dynamic fracture parameters. We propose a method to simultaneously measure these parameters for mode-I fractures in split Hopkinson pressure bar (SHPB) testing with a notched semi-circular bend (SCB) specimen. The initiation toughness is obtained from the peak load given dynamic force equilibrium. A laser gap gauge (LGG) is developed to monitor the crack surface opening displacement (CSOD) of the specimen, from which the fracture velocity and the fracture energy can be calculated. The feasibility of this methodology for coarse-grained solids is demonstrated with the SHPB-SCB experiments on Laurentian granite.     

A sandwich three-point bend specimen for testing mode-I interlaminar fracture toughness for fiber-reinforced composite materials

A sandwich three-point bend specimen has recently been proposed to test mode-I interlaminar fracture toughness for fiber-reinforced composite materials. The test composite consist of a thin layer bonded by two lateral reusable steel bars (Sohn et al. 1995). Some time earlier this specimen configuration was used to test fracture toughness of adhesives (Zdaniewsk et al. 1987). However, formulae for analysing its fracture mechanics parameters such as stress intensity factor and energy release rate can not be found in the literature. The lack of adequate formulae may explain why suitable quantitative analysis using this specimen configuration has not been achieved. In this paper, a simple and effective homogenisation method is used to change the bi-material system, which represents the specimen, into single uniform test material. This physical homogenisation is carried out by geometric change of the cross section of lateral steel parts based on equal deflection rigidity. For the transformed specimen configuration of single uniform material, the corresponding stress intensity factor solution from handbooks is available. Two formulae of stress intensity factor for the sandwich three-point bend specimen are given as upper limit and lower limit respectively, they are plotted with varying elastic tensile modulus mismatch. Then the relation between stress intensity factor and energy release rate, with special consideration of orthotropy of the tested composite material, is used to derive its energy release rate. The specimen and its formulae can also be applied to test other materials such as wood, welded joints (Burstow and Ainsworth, 1995), as well as to test dynamic fracture toughness. This revised version was published online in July 2006 with corrections to the Cover Date.     

Object Grating Method Application in Strain Determination on CTOD Tests

Abstract:  Standard fracture toughness tests require standard specimens with the presumption that mechanical properties are uniform in the crack growth direction. Standards for crack tip opening displacement (CTOD) fracture tests prescribe remote crack mouth opening displacement, which can lead to inadequate results in the case of heterogeneous materials properties. This paper describes the application of an object grating method (OGM) on the fracture behaviour of a heterogeneous specimen. Fracture behaviour is described by measuring deformation on the surface of a specimen, in terms of CTOD and, consequently, by strain determination. An OGM is advantageously used when measuring modified CTOD tests on two specimens with an initial crack in a macroscopic heterogeneous welded joint. Results significantly show that fracture behaviour depends on the material in the vicinity of the crack tip concerning the direction of crack propagation.     

Mode II fracture characterization of a hybrid cork/carbon-epoxy laminate

Fracture characterization under mode II loading of a hybrid laminate composed by a unidirectional carbon fiber-epoxy composite and cork was performed using the End Notched Flexure test. A data reduction scheme based on equivalent crack length concept, specimen compliance and Timoshenko beam theory was applied to evaluate fracture toughness under mode II loading of a composed beam (cork and carbon-epoxy composite). The adopted procedure depends exclusively on the data issuing from load–displacement (P–δ) curve and does not require crack length monitoring during the test which is a difficult task to be accomplished with the necessary accuracy in the ENF test. A numerical analysis using cohesive zone modeling and an inverse procedure was performed to assess the mode II cohesive law that simulates the material fracture under shear loading. It was concluded that hybridization is advantageous relative to monolithic carbon-epoxy laminate in which concerns the observed failure mode, which altered from typically brittle to very ductile thus contributing to avoid sudden shear failures in real applications.     

Toughness of aromatic polymer composites reinforced with carbon fibres

This experimental study focuses on the toughness of a thermoplastic composite, namely, poly ether-ether-ketone (PEEK) reinforced with 60% by volume of continous carbon fibres (APC 2). Toughness is assessed using both comparative and intrinsic techniques and a critical discussion of the two approaches is presented.The comparative toughness of cross-ply and quasi-isotropic sheets of APC 2 is studied using a damage tolerance test (compression after impact) and by using an instrumented falling weight impacr test over a range of temperatures. Intrinsic toughness is discussed by applying fracture mechanics techniques to unidirectional laminates. Double cantilever beam and three-point flexure tests are used, the latter being performed in six different crack directions. Fracture toughness results are presented for APC 2 and unreinforced PEEK.An ultrasonic C-scan on impacted specimens and scanning electron microscopy on fracture surfaces are used to explore further the mechanisms of fracture, e.g. delamination, fibre breakage and matrix cracking.     

Fracture mechanics approach to facesheet delamination in honeycomb: measurement of energy release rate of the adhesive bond

Two types of experiments were designed and performed to evaluate the adhesive bond in honeycomb sandwich panels. The tensile bond strength between the facesheet and the core was determined through the flatwise tension test. The fracture toughness of the bond line was measured through the double cantilever beam test. Fracture toughness values varied for different facesheet thicknesses and core materials. Toughness was also different for the bag and tool sides of the panels for all specimen types.     

On fracture toughness and its size dependence for steels showing thickness delamination

The effect of thickness delamination on fracture toughness has been studied. The test material used was a martensitic-austenitic pressure vessel steel. Tests were performed on compact tension and three point bend specimens of varying sizes. All specimens were machined from plate material of 100 mm thickness. It was found that the ASTM practice of test evaluation leads to a size dependence of fracture toughness although data for all specimens fulfill the ASTM size requirements. This size dependence has been explained theoretically and it was shown that an evaluation method based on a fixed absolute amount of apparent crack extension would lead to coinciding data for all specimen sizes.     

Bruchzähigkeit und Ermüdungs-Rißwachstum von Gußeisen

Fracture Toughness and Fatigue Crack Growth of Cast Irons Fracture toughness, elastic moduli and fatigue crack growth rates in air and in vacuum were measured for 17 different cast irons. The graphite shape in the cast irons varied from flakes to nodules, the matrix varied from ferrite to pearlite to martensite. In the fatigue crack growth rate tests, using fracture mechanics methods, it was observed that the fatigue crack growth rate increases significantly as the cyclic stress intensity range approaches the critical value for stable crack growth. This phenomenon was used to determine the fracture toughness of the cast irons. Such toughness data agree well with literature data on the fracture toughness of cast irons. An extensive review of the effects of strength on the fracture toughness of commercial cast irons is presented. In cast irons with flake graphite, cyclic loading results in a reduced modulus of elasticity. This is attributed to the rupture of the graphite flakes under cyclic loading.     

Ermittlung des Bruchwiderstands an Oxidkeramik und Hartmetallen mit verschiedenen Methoden

Fracture Toughness Determination of Alumina and Cemented Carbide with Different Testing Methods Fracture toughness of a sintered alumina and two tungsten carbidecobalt materials was determined using four-point-bend specimens with straight through and chevron notches and with the short rod specimen. With the specimens with a straight through notch a lower K_Ic was measured for Al₂O₃ and a higher for WC-Co compared to the chevron-notched specimens. This behavior was explained by the different shapes of the crack growth resistance curves and the different critical notch radii. For Al₂O₃ a steeply rising crack growth resistance curve was measured in a controlled fracture test, for WC-Co a flatter curve was obtained. The effect of the shape of the crack growth resistance curve and of notch width on the evaluated toughness is discussed.     

Estimation and comparative study of JIC using different methods for 20MnMoNi55 steel

Fracture toughness is one of the key input variables to compute critical load of the structural components. The resistance against ductile fracture can be quantified either by the initiation value or by the entire resistance curve. Different standard methods like J_SZW, JSME and ASTM: E1820 etc. are mainly used to estimate the critical crack initiation value from the resistance curve developed by the J-integral test. However, the results vary from method to method and are even inconsistent for the same method. Pehrson and Landes suggested a simple method for estimation of the critical fracture toughness by identifying the critical point corresponding to the maximum load on load–displacement curve. In the present study, different standard methods along with the one suggested by Pehrson and Landes are used to find out the critical fracture toughness using 1T–CT and ½T–CT specimens of the material 20MnMoNi55 steel for varying temperatures and crack size. The results are analyzed to compare the merits of the different methods of estimation of fracture toughness.     

Comparison of Interlaminar Fracture Toughness in Unidirectional and Woven Roving Marine Composites

This paper investigates the effect of fibre lay-up and matrix toughness on mode I and mode II interlaminar fracture toughness (G_Ic and G_IIc) of marine composites. Unidirectional and woven roving fibres were used as reinforcements. Two vinyl ester resins with different toughness were used as matrices. Results from both modes showed toughness variation that is consistent with matrix toughness. Values of G_Ic were not significantly influenced by fibre lay-up except at peak load points in the woven roving/brittle-matrix composite. Each peak load point, caused by interlocked bridging fibres, signified the onset of unstable crack growth. For unidirectional specimens, crack growth was stable and G_Ic statistically more reliable than woven roving specimens, which gave fewer G_Ic values due to frequent unstable crack growth. Mode II tests revealed that, except for crack initiation, G_IIc was higher in woven roving composites. This was due to fibre bridging, perpendicular to the crack growth direction, which encouraged stable crack growth and increased energy absorption. Mode II R-curves were obtained for the woven roving specimens. These R-curves provide additional information useful for characterising delamination resistance. The paper concludes that composites with woven roving fibres show similar mode I delamination characteristics to the unidirectional composites; but their mode II delamination characteristics, after crack initiation, are quite different.     

Die Messung der Bruchzähigkeit eines Vergütungsstahles mit Hilfe der Teilentlastungsmethode

Application of the Unloading Compliance Method in Fracture Toughness Measurements of a Quenched and Tempered Steel The application of the J-integral leads to a considerable reduction of material needed for establishing toughness data. The number of specimens is further reduced by measuring the crack resistance curve in a single specimen. This requires monitoring the crack extension during the experiment. A comparison of several methods showed that the unloading compliance technique is particularly suitable for that purpose. This method was applied for measuring the toughness as a function of location in a large forging of a steel 25 NiCrMo 14 5. Good toughness values (about 200 MPam^1/2) with little scatter were found over the whole cross section of the forging.     

Fracture toughness variability of structural steel

The weakest-link model of brittle fracture initiation has had substantial success in describing the inherent variability (scatter) in fracture toughness values for steel samples failing by cleavage. The model predicts a Weibull distribution of fracture toughness with slope 4 when plotted in the conventional fashion [E 1921-02. Standard test method for determination of reference temperature, T₀, for ferritic steels in the transition range. Annual Book of ASTM Standards, vol. 3.01. PA, USA: American Society for Testing and Materials; 2002]. However, the Weibull slope for samples of a structural steel tested at CANMET has been found to be 1.86, significantly less than the expected value of 4. Possible reasons for the discrepancy are discussed.     

低温环境下测试复合材料Ⅰ型层间断裂韧性的简易方法

目前ASTM复合材料Ⅰ型层间断裂韧性测试标准需不断观测裂纹扩展长度。然而在低温环境下,裂纹扩展长度不易测量且过程繁琐。为克服这一缺陷,本文采用双柔度法测试复合材料低温环境下Ⅰ型层间断裂韧性,该方法的步骤与ASTM标准基本相同,但不需观测裂纹扩展长度便能获得低温下Ⅰ型层间断裂韧性。为了验证该方法的可靠性和精度,采用5件碳纤维增强环氧树脂基复合材料双悬臂梁（DCB）试样在-10℃环境下进行Ⅰ型层间裂纹扩展实验,应用ASTM标准所推荐的三种方法及本文的双柔度法进行数据处理获得复合材料Ⅰ型层间断裂韧性。结果表明:ASTM标准的三种方法与双柔度法得到的Ⅰ型层间断裂韧性结果一致,相对差别小于5%,而本文的双柔度法不需测量裂纹扩展长度,因此更简单,为测试低温环境下Ⅰ型层间断裂韧性提供了一种准确、简单的新方法。      

木材断裂解离分形特征与分形断裂力学模型研究

目的 以椴木为研究对象,研究冲击载荷作用下椴木试件的断裂解离形貌特征和断裂力学特性,建立适用于木材原料断裂解离的分形断裂力学模型,并对其断裂解离力学行为进行描述。方法 对椴木试件进行冲击加载试验,分析试件断口的形貌特征和断裂力学特性,构建适用于木材原料断裂解离的分形断裂力学模型。结果 椴木试件横向冲击断裂断口裂纹形状和断口形貌特征比纵向冲击复杂,横、纵向冲击断裂断口均具有分形特征;椴木试件纵向冲击断裂韧性均值是横向冲击断裂韧性均值的1.112倍,椴木试件横、纵向冲击断口的分形维数均值分别为2.063 5和2.075 1,椴木试件横、纵向冲击韧性与其断口分形维数之间存在线性正相关关系,拟合优度分别为0.778 7和0.812 2;构建的木材原料断裂解离临界解离应力和断裂韧性的分形断裂力学模型也适用于脆性材料。结论 在木材原料冲击断裂解离时,木材原料初始裂纹长度越短,断裂解离断口越粗糙复杂,木材原料断裂解离所需要的能量越大;当裂纹沿着与冲击加载力方向垂直成大约1.055rad方向扩展时所需的能量最小,木材原料最易沿该方向进行断裂解离。     

Biaxiality Dependence of the Fracture Toughness for Glass in Plane Stress State

The fracture behaviour of glass in biaxial stress state has been investigated. Fracture toughness of disk specimen with a straight-through crack was measured under biaxial tension and uniaxial tension loads respectively. The difference between them and the reasons for the difference are discussed. The influence of the stress parallel to crack on fracture of brittle material was demonstrated in theory and experiments. The results show that plane stress fracture toughness of glass is not a material constant. and that the fracture toughness measured in biaxial tension state is higher than that measured under uniaxial tension. The conventional fracture criterion upon the stress intensity factor is questioned in the case of biaxial stress problem, and the strain dependence of crack growth is discussed.