2-D biaxial testing and failure predictions of IM7/977-2 carbon/epoxy quasi-isotropic laminates

In previous research, a series of a thickness-tapered cruciform specimen configurations have been used to determine the biaxial (two-dimensional, in-plane) and triaxial (three-dimensional) strength of several carbon/epoxy and glass/vinyl-ester laminate configurations. Refinements to the cruciform geometry have been shown capable of producing acceptable results for cross-ply laminate configurations. However, the presence of a biaxial strengthening effect in quasi-isotropic, [(0_N/90_N/ ± 45_N)_M]_S, laminates have brought into question whether the cruciform geometry could be used to successfully generate two-dimensional strength envelopes. In the present study, a two-dimensional failure envelope for a IM7/977-2 carbon/epoxy laminate was developed at the Air Force Research Laboratory, Space Vehicles Directorate, using a triaxial test facility. The electromechanical test frame is capable of generating any combination of tensile or compressive stresses in σ₁:σ₂:σ₃ stress space and can evaluate the uniaxial (one-dimensional, in-plane), biaxial or triaxial response of composite materials. Results are promising as they indicated that failure in the majority of the IM7/977-2 specimens occurred in the gage section. This leads the authors to believe that maximum biaxial stress states were correctly generated within the test specimen. In addition to the experimental data presented, multi-continuum theory (MCT) was used to predict and analyze the onset of damage and ultimate failure of a biaxially loaded IM7/977-2 laminate. Multi-continuum theory is a micromechanics based theory and associated numerical algorithm for extracting, virtually without a time penalty, the stress and strain fields for a composites’ constituents during a routine structural finite element analysis. Damage in a composite material typically begins at the constituent level and may, in fact, be limited to only one constituent in some situations. An accurate prediction of constituent failure at sampling points throughout the laminate provides a genesis for progressively analyzing damage propagation in a composite specimen allowing identification of intermediate damage modes. A constituent-based, quadratic, stress-interactive, failure criterion was used to take advantage of the micro-scale information provided by MCT. There was reasonable correlation between analytically and experimentally developed IM7/977-2 2D failure envelope which leads us to believe that the thickness-tapered cruciform specimen can be used to determine the biaxial strength of quasi-isotropic laminates.     

Notched strength of carbon fibre/epoxy composite laminates with a circular hole

This paper improves the two stress fracture criteria proposed by Whitney and Nuismer (known as the point stress criterion and the average stress criterion) to predict the strength of composite laminates with a circular hole. In the point stress criterion, it is assumed that the failure occurs when the stress over some distance (d ₀) away from the notch is equal to or greater than the unnotched laminate strength. In the average stress criterion it is assumed that failure occurs when the average stress over some distance (a ₀) ahead of the notch equals the unnotched laminate strength. Both stress fracture criteria are two parameter models based on the unnotched strength (σ₀) and a characteristic dimension (d ₀ or a ₀). A simple relation is used for the characteristic length to improve the accuracy while evaluating the notched strength of carbon/epoxy composite laminates. The analytical results are compared well with the existing test results of AS4-carbon/948 A1 epoxy [0/90]_{4 s} and [0/±45/90]_{2 S} composite laminates with various hole diameters and specimen widths.     

Notched strength of carbon fibre/epoxy composite laminates with a circular hole

This paper improves the two stress fracture criteria proposed by Whitney and Nuismer (known as the point stress criterion and the average stress criterion) to predict the strength of composite laminates with a circular hole. In the point stress criterion, it is assumed that the failure occurs when the stress over some distance (d ₀) away from the notch is equal to or greater than the un-notched laminate strength. In the average stress criterion it is assumed that failure occurs when the average stress over some distance (a ₀) ahead of the notch equals the unnotched laminate strength. Both stress fracture criteria are two parameter models based on the unnotched strength (σ ₀) and a characteristic dimension (d ₀ ora ₀). A simple relation is used for the characteristic length to improve the accuracy while evaluating the notched strength of carbon/epoxy composite laminates. The analytical results are compared well with the existing test results of AS4-carbon/948 Al epoxy [0/90]_4s and [0/ ± 45/90]_2S composite laminates with various hole diameters and specimen widths.     

Design of a cruciform specimen for biaxial testing of fibre reinforced composite laminates

To study the behaviour of fibre reinforced composite laminates under static and cyclic in-plane complex stress states, a biaxial loading frame has been developed. A cruciform type specimen is biaxially loaded in its plane using four independent servo-hydraulic actuators. An appropriate control unit keeps the centre of the specimen at the same position during the test. For obtaining reliable biaxial failure data the design of the cruciform specimen is of paramount importance. Finite element simulations of the cruciform specimen to study the influence of various geometrical parameters and experiments on nine selected cruciform specimen types using both strain gages and an optical-numerical full field method for strain determination over the entire biaxially loaded test zone have been carried out. In the present paper, the four most important geometries will be discussed. Since stresses in the biaxially loaded zone cannot be calculated from the experimentally applied loads due to the ill definition of the load bearing area, strain values – the only measurable quantity – are used for the comparison of the different geometry types. For the glass fibre reinforced composite material with a [(±45/0)₄/±45]_T lay-up this led to the proposal of an optimized geometry: a plane cruciform type specimen with a circular central region of reduced thickness and an adapted corner fillet at the intersection of the arms. Using this geometry failure will occur in the biaxially loaded test zone, rather than in the uniaxially loaded arms, at failure strains in the centre of the specimen comparable for the uniaxial load ratios to strains obtained on standard beam specimens. Tests at different load ratios were performed to obtain data as input for failure criteria. This paper focuses on the design of the specimen. In the near future, the biaxial test results will be compared with existing failure criteria.     

Experimental Evaluation of Mixed Mode Stress Intensity Factor for Prediction of Crack Growth by Phoelastic Method

Determination of stress intensity factors K _I, K _II, and constant stress term, σ _ox is investigated. A theory of determining the stress intensity factors using photo-elastic method is formulated taking three stress terms. Three-parameter method of fracture analysis for determining the mixed mode stress intensity factors under biaxial loading conditions from photo-elastic isochromatic fringe data is used. A special biaxial test rig is designed and fabricated for loading the specimen biaxially. A simplified and accurate method is proposed to collect the data from isochromatic fringes. Taking specimen geometry and boundary conditions into account, regression models are developed for estimation of fracture parameters.     

An experimental investigation of the effect of biaxial loading on the master curve transition temperature in RPV steels

During the 1990s considerable work was conducted to characterize the effect of biaxial loading on the ductile to brittle transition temperature. The work centered on a series of tests using large cruciform bend specimens from an experimental A533B test plate denoted as HSST Plate 14 (Heavy Section Steel Technology Plate 14). Recently a series of similar biaxial cruciform tests has been conducted on the steel used for an extensive European Round Robin that investigated the ductile-to-brittle transition master curve and associated T₀ reference temperature. The results of these tests have been used to promote the concept of a “Biaxial Effect” which corresponds to a shift in the shallow crack transition master curve of +20 °C or more when biaxial stresses are present, in comparison with the master curve for uniaxially loaded shallow crack specimens. A comprehensive analysis of the all of the available HSST Plate 14 data and data from two other structural steels was performed to investigate the extent of a biaxial effect on the reference temperature, T₀. The analysis included many additional biaxial cruciform test results on three different materials. The results of all three materials discussed in this paper fail to clearly demonstrate that biaxial loading, imposed through the use of a cruciform specimen geometry, has an effect on the fracture toughness, characterized using a master curve approach and reference temperature T₀. The analysis utilized in this paper assumes that the toughness distribution and temperature dependence of shallow cracked specimens can be modeled by using the master curve approach. This assumption has not been rigorously validated and would benefit from further study. Additional detailed stress analysis of the constraint evolution in the cruciform specimens may better define the precise conditions under which a biaxial effect on the fracture toughness could be realized.     

Fatigue strength of fillet welds subjected to multi-axial stresses

Fatigue endurance assessments of welded details are normally carried out by calculating the relevant stress acting on the detail and identifying a relevant fatigue class (or detail category) with its associated S–N curve. The fatigue strength of most structural details incorporated in design codes has been obtained from fatigue tests conducted under uni-axial loading conditions, which normally result in a uni-axial stress state in the detail. Many of the structural details that exist in fatigue-loaded structures experience some kind of multi-axial loading condition. The subject of the fatigue strength of welded details under multi-axial loads has been the topic of numerous research projects in recent years. The vast majority of these projects were, however, devoted to cracking in the base metal (i.e. toe cracking). Very little has been done with reference to the cracking of fillet welds in combined loading situations (i.e. root cracking). This paper presents new test results from cruciform specimens, in which weld failure initiated at the root in a multi-axial stress state. The tests have been performed at two different load levels and on three different specimen configurations giving different τ/σ ratios. This permitted an examination of the effect of the shear to normal stress ratio on the fatigue strength of fillet welds. The results of these tests, together with other relevant tests reported in the literature, are then evaluated in relation to the design models proposed in three design standards: Eurocode, IIW and DNV. No obvious dependence on the τ/σ ratios could be found. The evaluated models all appear to be able to predict the fatigue life of a cruciform weld failing from the root under combined shear and normal stress.     

Effects of geometry of notched specimens on the local cleavage fracture stress σf of C-Mn steel

An elastic-plastic three-dimensional finite element method analysis is used to determine the stress and strain distributions ahead of notches of four-point bending (4PB) specimens with various sizes (W, B and a) and widths (B). By measuring the location of the cleavage initiation sites for a C-Mn steel, the local cleavage fracture stress σ_f is accurately determined. With increasing specimen sizes and widths the fracture load P_f increases considerably, but σ_f remains nearly constant. The reason that the σ_f of the specimen with minimum size is slightly larger than that of the other specimens is analyzed by an active zone model of cleavage fracture for notched specimens. The critical event for cleavage fracture is the propagation of a ferrite grain-sized crack into the neighboring matrix, and is independent of specimen sizes and widths. σ_f is mainly determined by the length of the critical microcrack, and the specimen sizes and widths have little effect on it.     

Investigation of combined stress state failure criterion for glass fiber/epoxy interface by the cruciform specimen method

The interfacial failure criterion under combined stress state in a glass fiber/epoxy composite is investigated by the cruciform specimen method. Experiments were conducted by using specimens with a fiber whose angle from the loading direction is varied in order to make various stress state of normal and shear at the interface. Finite element analysis is performed to calculate the interfacial stress distribution. By combining the experimental measurement of the specimen stress at the interfacial debonding initiation and the finite element stress analysis, it is possible to obtain the interfacial stress state at interfacial failure. A method to determine the interfacial failure criterion and the interfacial failure initiation location simultaneously is proposed in the present study. We conclude the value of the interfacial shear strength is higher than that of the interfacial normal strength for the material system used in the present study.     

Fatigue strength of the Cu/Si interface in nano-components

The fracture behavior of the Cu/Si interface in a nano-cantilever specimen with a 200 nm-thick Cu film (Specimen-200), which possesses a nanometer-scale strain-concentrated region, is examined under a cyclic bending load. The fatigue strength is around GPa level owing to the high yield stress of the Cu nano-film and the deformation constraint associated with the neighboring hard materials. The S-N curve shows clear dependence of fatigue life on the applied stress in the high-stress range, Δσ. Specimens with a 20 nm-thick Cu film (Specimen-20) are also investigated for comparison. The stress range in the fatigue fracture of Specimen-20 is higher than that of Specimen-200 for the same fatigue life. However, there is good coincidence in the Δσ/σ_s (σ_s: strength in monotonic load) vs. N_f (number of cycles to fracture) at high Δσ. The S-N curves suggest the existence of a fatigue threshold (Δσ_w) at low Δσ. The ratio of fatigue limit to the fracture stress in a monotonic loading, Δσ_w/σ_s, is large compared with the magnitude of bulk metal, which suggests the brittle behavior of the interface. Moreover, the fatigue limits have good coincidence with their yield stresses.     

Langzeit- und Dauerschwingfestigkeit des Vergütungsstahls 25CrMo4 bei mehrachsiger Beanspruchung durch drei schwingende Lastspannungen

High-Cycle and Long-Life Fatigue of 25CrMo4 under Multiaxial Load Conditions by three Alternating Stresses Statistically verified experimental results from high-cycle and long-life fatigue tests (HCF and LLF) with altogether 537 unnotched solid cylindrical and thin-walled hollow specimen are demonstrating the fatigue behaviour (S-N-characteristics, scatterband) of 25CrMo4 under uniaxial loading with superimposed static stresses (consideration of the mean stress effect) and under biaxial loadings in variation of phase differences between the three combined normal and torsional stresses σ_x, σ_y, τ_xy The fatigue strength is commonly decreasing with life time in the high-cycle regime until reaching the fatigue endurance limit in the transition range to infinite life. The “ductility level” τ_w/σ_w and the “mean stress sensibility” p = p (σ_w, σ_zSch, R_m) are relatively independent of the intensity by stress amplitudes and fatigue life to failure. In comparision with the specific case of biaxial combined loading with synchroneous amplitudes, the fatigue resistance characteristics are detrimentally influenced by out-of-phase normal stresses σ_x, σ_y; a phase difference of 180° between the normal stress amplitudes is the most critical state of combination, especially in the lower cycle regime caused by a greater slope coefficient (probability of survival P_s = 50%). On the contrary is there in the high-cycle regime as well as in the long-life range no significant influence to the fatigue strength by biaxial load conditions of simultaneously normal stresses with out-of-phase torsional stress τ_xy     

Creeping damage around an opening in rock-like material containing non-persistent joints

The purpose of this study is to investigate experimentally the creeping damage and failure mechanism around an opening in rock-like material containing non-persistent joints. The jointed rock-like specimen is modelled by plaster material, and the underground excavation is simulated by drilling at a certain stress level. In our experimental studies, time evolutions of deformation are recorded at various applied vertical (σ₁) and confining (σ₃) stress. It is found that with a fixed σ₁, tensile mode of creeping failure is dominant when the λ (σ₃/σ₁) is low (λ=1/3). But when λ is high (?1/2), shear mode of creeping failure is dominant. The creeping failure time decreases with the increased λ and stress ratio of σ₁/σ_1max (σ_1max is the maximum stress of a jointed rock-like mass). Furthermore, for the excavation in a low stress level (σ₁/σ_1max?45%), no creeping damage around opening will occur. The stress ratio λ and σ₁/σ_1max are the important indices indicating the degree of instability of an opening after excavation.     

Slip initiation on frictional fractures

Direct shear tests and biaxial compression tests are conducted to investigate the onset of slip along a non-homogeneous frictional surface and to determine the effect of specimen thickness and confining stress on slip initiation and propagation. The specimens are made of two and three acrylic blocks with the contact surfaces between blocks having on their upper half a frictional strength smaller than on their lower half. This creates a “weak” surface on the upper half and a “strong” surface on the lower half. The specimens are then loaded in direct shear or biaxial compression with confining pressures ranging from 0.7 to 3.5 MPa. The onset of slip, slip propagation, and the stress field generated at the front and center of the blocks interfaces are monitored using a photoelastic technique where a thin photoelastic film is placed at the location where observations are made. The onset of slip at the weak-strong zone interface is treated as propagation of a frictional crack under Mode II loading. The critical stress intensity factor, K_IIC, at the onset of slip is obtained from photoelastic techniques. The results show a weak dependency of K_IIC on the normal stress applied and no influence of the specimen size for specimens thicker than 25.4 mm; for thinner specimens the K_IIC values are smaller because the boundaries of the specimen prevent the full development of the stress field ahead of the crack tip. The experiments show a linear increase of the critical energy release rate with normal stress which is explained with linear elastic fracture mechanics theories.     

Fatigue behaviour of a box-welded joint under biaxial cyclic loads

Multiaxial fatigue behaviour of box-welded (wrap-around) joints in a JIS SM400B steel (12-mm-thick plate) was examined using a biaxial fatigue test facility. For the specimen, two stiffeners were attached to a main plate by a CO₂ semi-automatic welding procedure. Residual stress measurements and finite element (FE) analyses were also performed. Fatigue tests were performed under both uniaxial and biaxial (mainly out-of-phase) cyclic loads, and both results were compared and examined. It was found that fatigue cracks in the biaxial fatigue test specimens were initiated at the boxing-weld toes and propagated almost in the direction of the lateral loads. This is considered to be due to the dominant direction of tensile residual stresses from welding and the stress concentration in the vicinity of the boxing-weld toe. From the relation between the strain range near a weld toe, Δε₅ , and the fatigue lives, it was found that crack initiation life, N_c , was almost equivalent in the biaxial and uniaxial fatigue tests, while the failure life, N_f , was slightly longer in the biaxial tests. However, when the fatigue lives are put in order using the stress range near a weld toe, Δσ₅ , the crack initiation life, N_c , in the out-of-phase biaxial tests (phase difference of π) is ~30% lower than in the in-phase biaxial and uniaxial tests, while the failure life, N_f , was almost equivalent in the biaxial and uniaxial tests. From these results, it is concluded that an increase in Δσ₅ (lowering of the minimum value of σ₅ ), induced by the out-of-phase lateral loads, leads to an increase in fatigue damage where the high tensile welding residual stresses exist in the vicinity of the boxing-weld toe. Finally, a simple life estimation for the biaxial fatigue tests was made using FE analyses and the results of the uniaxial fatigue tests, proving that the effects of the lateral loads should be taken into consideration.     

The characteristics of an inclined crack in anisotropic paperboard under biaxial loading

In this paper, a fracture mechanics method was applied for the evaluation of crack behaviour in anisotropic paperboard subjected to biaxial uniform loading. The experiment was performed to determine the crack propagation angle and the fracture strength of paperboard under biaxial loading with the cruciform specimen optimized by FEM simulation. The effects of biaxial loads on the critical stress ratio and crack propagation angle for various inclination angles were investigated. The experimental results were compared with theoretical results, which were calculated by using the Normal Stress Ratio Criteria. The experimental results for crack propagation angle and critical stress show good agreement with theoretical results.     

Mixed-Mode Crack Propagation in Cruciform Joint using Franc2D

The focus of this research was on determining the cracking behavior when parameter such as the biaxiality ratio was varied. The crack propagation under mixed-mode loading was simulated by means of finite element method. The stress intensity factors have been calculated by the linear elastic fracture mechanics approach using fracture analysis code-2D (Franc2D). The crack growth under opening mode-I was considered because the crack growth occurs mainly along the direction where the mode-I stress component becomes the maximum. The numerical integration of Paris’ equation was carried out. The effect of normal and transverse applied load (σ _x, and σ _y, respectively) on crack propagation was presented. It was found that the fatigue crack growth was faster at a smaller biaxial stress ratio (λ), i.e., higher σ _y on the horizontal crack plan. Moreover, fatigue strength values decrease as λ decreases. The results confirm the use of fracture mechanics approach in biaxial fracture.     

SiC/Ti-6Al-4V复合材料在横向拉伸载荷下界面失效行为的数值模拟

采用有限元模拟了SiC/Ti-6Al-4V复合材料冷却过程和横向拉伸试验过程, 横向拉伸试样采用十字形试样。分别建立了平面应力和轴对称有限元模型, 采用平面应力有限元模型计算环绕纤维圆周的界面微区应力分布, 预测界面失效机制。采用轴对称有限元模型分析复合材料界面脱粘过程以及残余应力对界面径向应力分布的影响。结果表明: 对于SiC/Ti-6Al-4V复合材料十字形试样,在横向拉伸载荷下的界面失效由径向应力导致,界面失效模式为法向失效, 剪切失效模式未发生; 十字形试样在横向拉伸载荷下界面初始脱粘位置处于界面中间; 随横向拉伸应力增加, 十字形试样的界面脱粘对称向两边扩展; 界面径向应力随残余应力降低而升高。     

含孔CFRP正交层合板的双轴拉伸力学行为

采用加载臂开槽的中心开孔等厚度十字形试样,实验研究了正交对称铺层碳纤维增强聚合物基复合材料（CFRP）层合板在双轴拉伸载荷作用下的力学行为,分析了3种双轴加载比对其拉伸强度和破坏行为的影响。研究表明:纤维被切断的铺层部分在拉伸作用下容易与其相邻铺层脱粘,导致层合板承载力下降;等双轴加载时,在孔边的被切断纤维与连续纤维间基体在横向拉伸和纵向剪切组合作用下首先开裂;非等双轴加载时,在垂直于快速拉伸方向的铺层中沿孔边应力集中处先出现基体裂纹;随着加载比的增大,快速拉伸方向的细观结构损伤随载荷的增大发展更快,刚度下降更快,破坏时主裂纹的扩展方向更趋于垂直于快速拉伸方向;强度包络线的分析表明快速拉伸方向的拉伸强度随加载比的增大呈缓慢增大的趋势。      

A survey of test methods for multiaxial and out-of-plane strength of composite laminates

This review paper gives an overview of test methods for multiaxial and out-of-plane strength of composite laminates, with special consideration of non-crimp fabrics (NCF) and other textile systems. Tubular and cruciform specimens can provide arbitrary in-plane loading, while off-axis and angle-ply specimens provide specific biaxial loadings. Tensile and compressive out-of-plane strength may be determined by axial loading of specimens with a waisted gauge section, while bending of curved specimens allow determination of the out-of-plane tensile strength. Tests suited for out-of-plane shear strength include the short beam shear test, the inclined double notch test and the inclined waisted specimen. Testing of arbitrary tri-axial stress states using tubular or cruciform specimens with superimposed through-the-thickness loading is highly complex and significant problems have been reported in achieving the intended stress states and failure modes. Specific tri-axial stress states can be obtained by uniaxial loading of specimens with constrained expansion, as in the die channel test.     

Effects of deposition conditions of the Al film in Al/glass specimens and annealing conditions on internal stresses and hillock formations

In the present study, 25 kinds of specimen with five Al-film thicknesses were prepared to investigate the relation between the internal stress formed during the annealing process and the hillocks. In the preparation of specimens, the governing factors including deposition conditions, annealing temperature, and annealing time, were arranged following the orthogonal table of five-level and six-factorial (L₂₅(5⁶)) design. Stoney's formula is applied to describe the internal stresses before and after annealing (σ₀ and σ_f), respectively. The internal stress arising during the annealing process (σ_an) is evaluated using the model developed by Flinn et al. [1]. Then, the response surface methodology (RSM) is used to express the three stress parameters in terms of influential factors. The incipient σ_an value for hillocks appearing in the specimens was found to be between − 28.7 MPa and − 32 MPa in a compressive form. The annealing temperature, time, and Al-film thickness are the three major factors, affecting internal stress σ_an. An increase in the annealing time reduces the tensile stress or increases the compressive stress, or both. The tensile stress decreases and the compressive stress increases during the annealing process with increasing Al film thickness and annealing temperature. The number of hillocks formed in a unit of area is linearly proportional to both σ_an and (σ_f − σ_an).