The fracture behaviour of notched specimens of polymethylmethacrylate

The fracture behaviour of notched specimens of polymethylmethacrylate has been examined for a wide range of geometries in Charpy impact tests, and in tensile and slow bend fracture tests. It was found that the failure of the very sharply notched specimens was consistent with linear elastic fracture mechanics and defined a constant fracture toughness K _IC for a constant notch tip radius, whereas the blunt notched specimens failed at a constant critical stress at the root of the notch.     

Q690D高强钢基于连续损伤模型的断裂破坏预测分析

高强钢材在实际钢结构中已经开始逐步得到应用,该文针对Q690D高强度结构钢材,进行了钢材圆棒试样在单调加载和超低周循环加载下的断裂破坏试验,研究了试样裂纹的起始位置,分析了加载制度对试样承载能力和变形能力的影响,并采用扫描电镜观察了试样断口的微观形貌,断口呈现韧窝形式的延性断裂特征。基于Q690D钢材缺口圆棒试样的单调拉伸试验结果,结合有限元分析,标定了钢材的连续损伤模型参数。最后,应用钢材的连续损伤模型,对圆棒试样和带初始间隙试样在不同加载制度下的断裂破坏进行预测分析,得到试样的裂纹起始位置、荷载-位移曲线、断裂位移和疲劳寿命均与试验结果吻合良好。     

预报三向碳碳材料在大偏轴角拉伸时的切口强度模型

三向碳碳材料在大偏轴角拉伸时,用纤维束的剪切强度来确定其切口强度,不会招致太大误差。先测定纤维束的剪切强度和基体碳的剪切强度,然后把3DC/C看成为正交异性均匀材料作平面力分析求得离切口较远处的位移场,以此为边界条件,求切口尖端附近的三维应力场。用Zweben的统计准则求出三向碳碳材料在大偏轴角拉伸下的切口强度,并用实验验证。      

LIFE PREDICTION BY SIMULATION OF CRACK GROWTH IN NOTCHED COMPONENTS WITH DIFFERENT MICROSTRUCTURES AND UNDER MULTIAXIAL FATIGUE

A modelling procedure was developed which is applicable to crack growth in notched components subjected to multiaxial fatigue for materials with different microstructures. An algorithm for crack growth, in a microstructure that was modelled as hexagons, was established as a competition between growth by crack linkages during the crack initiation and propagation stages and the propagation of a dominant crack as a single crack. Analytical results simulated by using the developed model were compared with experimental results from fatigue tests which had been conducted using notched specimens of pure copper, carbon steel and two kinds of titanium alloy. Cracking morphology, which was experimentally observed to depend on the microstructure and the loading mode, was well simulated using the present model. The fatigue failure life of a notched specimen was statistically estimated by a Monte Carlo procedure based on the model. The simulated life with a statistical scatter-band almost coincided with the experimental data.     

Damage mechanics of composite materials: I— Measurements of damage and strength

A new approach for modelling the strength of notched composites has been developed. The approach is based on the assumption that subcritical damage modifies the notch-tip stress field and that the state of subcritical damage just before failure, referred to as the terminal damage state (TDS), must have a significant influence on notched strength. The TDS was monitored for a wide range of cross-ply graphite reinforced epoxy specimens using real-time radiography. A finite element model incorporating the TDS was used to determine the modified notch-tip stress field. A simple tensile stress failure criterion has been found to predict failure very well provided that the effect of subcritical damage is considered in this way. The effect of both layup and notch size on strength can be entirely accounted for by the effect these parameters have on the terminal damage state. In the first paper of a four-part series, radiographs of c. 60 specimens have been used to characterize the notch-tip damage zone and to establish a qualitative relationship between terminal damage and notched strength.     

Notch effect on creep–fatigue life for Sn–3.5Ag solder

This paper studies the creep–fatigue crack initiation and failure lives of Sn–3.5Ag solder notched specimens focused on the multiaxial strain at the notch root. Push–pull creep–fatigue tests were performed using three circumferential notched specimens using four kinds of creep–fatigue strain waveforms. Multiaxial strains at the notched section were calculated by finite element (FE) analysis under four kinds of creep–fatigue loading. Creep–fatigue damage laws were applied for evaluating the crack initiation and failure lives using the multiaxial strains obtained by the FE analysis. von Mises equivalent strain at the notch root estimated the crack initiation lives with a large scatter as well as the failure lives. Instead, the mean value of von Mises equivalent strain over the cross section of the notch root estimated the crack initiation and failure lives with a small scatter.     

A new method for modelling the support effect under rotating bending fatigue: application to Ti‐6Al‐4V alloy,with and without shot peening

The subject of this paper is to investigate the capability of the relative stress gradient to properly represent the beneficial effect of residual stress states on the fatigue life of Ti‐6Al‐4V specimens, with notches of different severity. The research was developed considering notched and un‐notched specimens with different geometries and different shot‐peening treatments. The results were determined by running fatigue experimentation under rotating bending and by developing a novel predictive model based on the relationship between the local fatigue limit and a generalized form of the relative stress gradient, accounting for the peening‐induced residual stresses. The proposed tool for fatigue limit estimation was completed by a stochastic analysis, which considered the variability of the involved parameters, in particular the residual stress entity. This made it possible to finally determine the component failure probability in a general, efficient and accurate way.     

Interaction between anisotropic plastic deformation and damage evolution in Al 2198 sheet metal

Deformation anisotropy of sheet aluminium alloy 2198 (Al-Cu-Li) has been investigated by means of mechanical testing of notched specimens and Kahn-type fracture specimens, loaded in the rolling direction (L) or in the transverse direction (T). Fracture mechanisms were investigated via scanning electron microscopy. Contributions to failure are identified as growth of initial voids accompanied by a significant nucleation of a second population of cavities and transgranular failure. A model based on the Gurson-Tvergaard-Needleman (GTN) approach of porous metal plasticity incorporating isotropic voids, direction-dependent void growth, void nucleation at a second population of inclusions and triaxiality-dependent void coalescence has been used to predict the mechanical response of test samples. The model parameters have been calibrated by means of 3D unit cell simulations, revealing the interaction between the plastic anisotropy of the matrix material and void growth. The model has been successfully used to describe and predict direction-dependent deformation behaviour, crack propagation and, in particular, toughness anisotropy.     

Identifying the linear cracking resistance characteristics for normal detachment in a composite

Summary A method has been devised for determining the structural characteristics of the cracking resistance for an orthotropic composite on a rectangular specimen having a central notch, which includes calculations on the state of strain in the notched specimen and determination of the structural-element dimensions, as well as choosing specimens for tests and determining the failure loads, followed by statistical processing.Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 26, No. 3, pp. 59–65, May–June, 1990.     

A STATISTICAL MULTI-SITE FATIGUE DAMAGE ANALYSIS MODEL

A statistical model has been developed to evaluate fatigue damage at multi-sites in complex joints based on coupon test data and fracture mechanics methods. The model is similar to the USAF model, but modified by introducing a failure criterion and a probability of fatal crack occurrence to account for the multiple site damage phenomenon. The involvement of NDI techniques has been included in the model which can be used to evaluate the structural reliability, the detectability of fatigue damage (cracks), and the risk of failure based on NDI results taken from samples. A practical example is provided for rivet fasteners and bolted fasteners. It is shown that the model can he used even if it is based on conventional S-N coupon experiments should further fractographic inspections be made for cracks on the broken surfaces of specimens.     

Damage mechanics of composite materials: II— a damaged-based notched strength model

A new model of the notched strength of graphite-epoxy composites has been developed. In this second paper of a four-part series, a finite element model has been used to simulate observed subcritical notch tip cracking patterns in cross-ply laminates. The model produced maps displaying tensile stress contours in the 0° ply, and it was found that all specimens failed when the maximum tensile stress in the 0° ply exceeded the strength of that ply. The strength of the 0° ply in the vicinity of the notch tip was determined independently using a Weibull statistical strength model.     

Behavior of notched and unnotched [0/±30/±60/90]s GFR/EPOXY composites under static and fatigue loads

The main objective of the present paper is to study the bending behavior of notched and unnotched angle-ply, [0/±30/±60/90]_s, glass fiber reinforced epoxy (GFRE) composites under static and fatigue loads. Static and fatigue bending properties have been determined for notched and unnotched angle-ply specimens. For this purpose different circular notch sizes (2, 4.5, 7, 9 mm) were drilled at the specimen center. Constant-deflection bending fatigue tests were performed at zero mean stress and 25 Hz. A 15% reduction of the initial applied moment was taken as a failure criterion. S–N diagrams for notched GFRE specimens have been constructed based on gross and net cross-section area. The results show that the ultimate bending strength of notched GFRE specimens decreased linearly with increasing notch diameter. Based on gross-section the fatigue life increases with decreasing notch size and the longer fatigue life was for the unnotched specimens. On the other hand, the S–N diagrams based on net-section indicate the insensitivity of angle-ply composites to the notch size. This is considered to be a peculiar phenomenon to composite materials. The results also show that the S–N diagrams have not any fatigue limit rigorous within 10⁷ cycles.     

INVESTIGATION OF THE ROLE OF RESIDUAL STRESSES IN THE WARM PRESTRESS (WPS) EFFECT. PART II—ANALYSIS

Abstract— Curry's model of the WPS effect has been applied to the results of a previous paper, and is extended to treat warm prestressing in blunt notched test-pieces. The effect of more complex prestress cycles is also predicted by an extrapolation of the model. The effects of the load-cool-fracture, LCF, cycle can be reasonably predicted for both sharply precracked and blunt notched specimens. For the sharply precracked specimens the effects of the load-unload-cool-fracture, LUCF, cycle at — 196°C are consistently overpredicted and this may be due to a decrease in the cleavage fracture stress at — 196°C of the material at the crack tip which has been subjected to repeated plastic straining by the combination of loading cycles. Modifications to the model are suggested which reduce the overproduction but a wide degree of scatter is observed in the experimental observations. Blunt notched specimens show a reasonable correlation between prediction and theory for the tensile LUCF cycle. Problems have been found in predicting the effect of various prestress cycles in different specimens due to the inherent variability in baseline fracture behaviour of the weld metal. It is concluded that the general trend of results is adequately explained by superposition models but that a greater understanding of local flow properties at a crack tip is required to achieve reasonable predictive success for weld metals such as A533BW.     

Numerical investigation of progressive damage and the effect of layup in overheight compact tension tests

This work describes a numerical investigation into progressive damage development in notched fibre-reinforced composite laminates. A finite element approach is used which explicitly models the sub-critical damage in the form of delamination and splits using interface elements, and fibre failure using a progressive statistical failure theory. Failure predictions were made for Overheight Compact Tension (OCT) test specimens using five different layups made up from IM7/8552 carbon/epoxy pre-preg. Owing to the detailed modelling of the individual damage modes, their interaction is well characterised. The numerical results obtained compare well with detailed test observations, capturing delamination, intraply splitting and fibre breakage. By including the subcritical damage that occurs at the notch tip in the model, it is able to represent the effect on the stress concentration and hence to predict ultimate specimen failure.     

Statistical analysis and reliability prediction with short fatigue crack data

This paper proposes a probability model to describe the growth of short fatigue cracks. The model defines the length of each crack in a specimen as a random quantity, which is a function of randomly varying local properties of the material microstructure. Once the model has been described, the paper addresses two questions: first, statistical inference, i.e. the fitting of the model parameters to data on crack lengths; and secondly, predicting the future behaviour of observed cracks or cracks in a new specimen. By defining failure of a specimen to be the time at which the largest crack exceeds a certain length, the solution to the prediction problem can be used to calculate a probability that the specimen has failed at any future time. The probability model for crack lengths is called a population model, and the statistical inference uses the ideas of Bayesian statistics. Both these concepts are described. With a population model, the solution to statistical inference and prediction requires quite complicated Monte Carlo simulation techniques, which are also described.     

A tensile stress criterion for cleavage in precracked,notched and smooth bars

Using a statistical model derived for cleavage induced by hard particles, an analysis has been carried out of a newly defined critical tensile stress for cleavage, i.e. the statistical mean stress with respect to cleavage fracture probability. The results of the analysis show that the critical tensile stress (cleavage stress) is highest for a precracked bar, intermediate for a notched bar and lowest for a smooth bar, owing to the fact that small particles are possible to trigger cleavage when stress distribution in a bar is uneven. The cleavage stress for the precracked bar is found to decrease rapidly with increasing temperature while those for the notched and smooth bars remain almost constant. The cleavage stresses for the precracked, notched and smooth bars can be correlated through a definite formula. For a pure-bending notched bar, the conventional cleavage stress (maximum stress in the bar) is found to be a good approximation of the new cleavage stress. The difference between the two will increase when stress gradient becomes steeper.     

Anisotropic ductile failure in free machining steel at quasi-static and high strain rates

Leaded Free Machining Steel (FMS) specimens were tested in tension at quasi-static and high strain rates in both the longitudinal and transverse directions with respect to the axis of the bar material. For the quasi-static tests, a high degree of anisotropy of fracture behaviour was observed for both plain (unnotched) and notched specimens. However the difference in fracture strains for longitudinal and transverse directions was significantly reduced for the high stress triaxiality conditions produced by the sharper notches. Plain specimens tested at dynamic strain rates (10³ s⁻¹) failed at somewhat higher strains than those tested quasi-statically. For the notched specimens tested dynamically, there was a transition to a brittle mode of failure and there was no statistically significant anisotropy in the very low strains to failure recorded. These experimental results were linked to numerical predictions of the local stress, strain and strain rate conditions in the specimens carried out using a modified Armstrong–Zerilli constitutive model for the FMS. Changes in the percentage area and aspect ratio of the lead inclusions which act as sites for void growth under ductile failure conditions were measured for both longitudinal and transverse directions of loading. It was found that the apparent area of inclusions increases with degree of deformation due to void growth but that the aspect ratio decreases due to the inclusions/voids becoming more spherical. This effect was greater for loading in the transverse direction indicating that voids grow more readily from inclusions when the latter are aligned perpendicular to the direction of loading.     

Ductile rupture of A508 steel under nonradial loading

This study deals with the effect of loading path on the strain to failure of a C-Mn-Ni-Mo steel. The tests are carried out at 373 K on axisymmetric, notched tensile specimens calculated by the finite element method. Specimen geometries containing different notch radii and leading to widely different stress triaxiality ratios are investigated. The effect of nonradial load path is studied using relatively sharply notched specimens. It is shown that a simple linear damage rule does not account for the experimental results. A model based on the critical cavity void growth rate calculated from the Rice and Tracey model is shown to give results consistent with the experiments provided that the effect of prestrain on constitutive equation and on the stress triaxiality ratio is properly taken into account. The experimental results are also compared to a model based on continuum damage mechanics.     

A MULTIAXIAL FATIGUE STRAIN ENERGY DENSITY PARAMETER RELATED TO THE CRITICAL FRACTURE PLANE

The cyclic strain energy density parameter W for the critical or failure plane has been successfully applied in predicting the multiaxial fatigue life of an iron-base and a nickel-base alloy. This parameter has the advantage of being independent of loading condition, allowing a universal energy-life curve to be determined for a variety of torsion, tension and bending stress and strain states. The critical strain energy density parameter has been verified using experimental data obtained from tubular and notched specimens of SAE-1045 steel and Inconel 718.     

Mechanism of anisotropy in fracture behaviour and fracture toughness of high strength aluminium alloy plate

Abstract

The fracture behaviour and J_Ic fracture toughness of a commercial Al–Zn–Mg–Cu alloy plate has been investigated. Based on the experimental results and available theoretical analyses, the following results were obtained. Secondary grain boundary cracks appeared ahead of the main crack, which served as a triggering mechanism for small scale shearing. Shear failure facets on the fracture surface of single edge notched bend specimens represent the same type of fracture as the fast shear failure that occurred during tensile tests on notched specimens. The grain boundary cracking–small scale shearing mechanism is essentially a type of shielding event that not only makes the fracture appearance obviously anisotropic, but also, to a considerable extent, accounts for the strong anisotropy of fracture toughness.

MST/1111