Normal Stress Failure Criterion Research Articles

Interface crack growth rate and fatigue life of multilayer-coated conductor tapes

Rare-earth barium copper oxide (REBCO) coated conductor (CC) tapes in high-field magnet applications usually experience fatigue due to a variety of cyclic mechanical and thermal loads. Therefore, estimation of the fatigue life of a particular REBCO CC is vital for the successful development and applications of high-field magnets devices, which are crucial components for aerospace, automotive, and maglev train transportation. For these needs, the authors evaluated the interfaces fatigue crack growth rate, and fatigue life of multilayered yttrium barium copper oxide (YBCO) coated conductor (CC) tape at room temperature via a displacement-energy model (DEM) approach. The DEM approach can measure the damage initiation and propagation rate in specific interfaces of a multi-layer film structure simultaneously. It assumed transverse intrinsic tensile/compressive cyclic loading and adopted the linear-elastic damage law with the maximum normal stress failure criterion to characterize the degradation in the tape. With an initial Eigenfunction (W0) (a parameter equivalent to the stress loading amplitude range) set as 2.30 × 10-12 m, the computed results show a strain (ε) range from 0.35 to 0.46 % and fatigue ratio range from 0.002 to 0.07 in the interfaces of the tape. Under the given parameters, it was found out that the tape has a critical interface fatigue crack growth rate of 2.54 pm/cycle corresponding to fatigue life of 3.9372 × 105 cycles. According to our previous studies, the results on the DEM approach has good agreement with those on the Finite Element Method (FEM) counterpart model, closed-form solution (CFS) model, and X-ray diffraction method (XRD). This technique can help to avoid enormous resources usually spent experimentally on the calculation of fatigue life of REBCO CC tapes.

Failure of fiber-reinforced composite laminates under longitudinal compression

A micro-mechanics approach is put forward to predict the fiber kink inclination angle and the strength of a unidirectional composite under longitudinal compression. Internal stresses of constituent materials in the kink-band are calculated through Bridging Model; thus, only the constituent fiber and matrix properties of the composite are needed. Considering the non-uniform stress distribution caused by the embedded fiber, the homogenized stresses of the matrix are converted into true values with stress concentration factors before being used for failure analysis. The definition and application of stress concentration factors are introduced. A failure criterion based on Mohr’s theory is established to determine the orientation of potential failure surface and the failure situation of matrix, whereas a maximum normal stress failure criterion is used to detect the fiber breakage. The longitudinal compressive strength of a laminate is defined as the applied load at the moment when a failure of whichever constituent materials occurs first. The practicability and accuracy of the theory have been verified with a comparison between the predictions and the measurements obtained from the worldwide failure exercises and some other literatures.

V-notch tip subjected to in-plane mixed mode loading: overview of recent results and possible future outcomes

The fictitious notch rounding concept is applied for the first time to V-notches with root hole subjected to in-plane mixed mode loading. Outof- bisector crack propagation is taken into account. The fictitious notch radius is determined as a function of the real notch radius, the microstructural support length and the notch opening angle. Due to the complexity of the problem, a method based on the simple normal stress failure criterion has been used. It is combined with the maximum tangential stress criterion to determine the crack propagation angle. An analytical method based on Neuber's procedure has been developed. The method provides the values of the microstructural support factor as a function of the mode ratio and the notch opening angle. The support factor is considered to be independent of the microstructural support length. Finally, for comparison, the support factor is determined on a purely numerical basis by iterative analysis of FE models.

A review of the notch rounding approach under in plane mixed mode loading

The fictitious notch rounding approach is widely used for the fatigue assessment of welded joints and for this reason in the present paper a review of the concept applied to inclined lateral V-notches with root hole subjected to in-plane mixed mode loading has been carried out. This is the basis for future applications to welded structures in presence of mixed mode loading.The analytical framework of the method is herein recalled and the fictitious notch radius is determined as a function of the real notch radius, the microstructural support length and the notch opening angle. In order to reduce the complexity of the task, we adopt a method based on the normal stress failure criterion. The method provides the values of the microstructural support factor as a function of the mode mixity parameter and the notch-opening angle. Moreover, the support factor is assumed independent of the microstructural support length. Finite element simulations for various notch shape and configurations are compared to experimental data from pointed V-notches made of polymethylmethacrylate. The model prediction showed good agreement with the experimental results. These results are very promising for the application to welded structures.

Tilted lateral V-notches with root hole subjected to in-plane mixed mode loading: Fictitious notch rounding concept

The fictitious notch rounding concept is applied for the first time to inclined lateral V-notches with root hole subjected to in-plane mixed mode loading. Out-of-bisector crack propagation is taken into account by combining the fictitious notch rounding approach with the maximum tangential stress criterion. Following the guidelines of a previous paper dealing with internal notches, the fictitious notch radius is determined as a function of the real notch radius, the microstructural support length and the notch opening angle. The problem is of formidable complexity and for this reason a simple method based on the normal stress failure criterion is adopted here. The analytical method based on Neuber's procedure proposed for central notches is extended here to tilted lateral notches. The method provides the values of the microstructural support factor as a function of the mode mixity parameter and the notch opening angle. The support factor is considered to be independent of the microstructural support length. To validate the approach about two thousands finite element analyses have been performed varying the notch shape and load configuration. Finally an experimental validation has been performed considering a complete set of data from pointed V-notches made of polymethylmethacrylate.

Crack Initiation at V-Notch Tip under In-Plane Mixed Mode Loading: A Review of the Fictitious Notch Rounding Concept

The fictitious notch rounding concept has been recently applied for the first time to V-notches with root hole subjected to in-plane mixed mode loading. Out-of-bisector crack propagation is taken into account. The fictitious notch radius is determined as a function of the real notch radius (the microstructural support length) and the notch opening angle. Due to the complexity of the problem, a method based on the simple normal stress failure criterion has been used. It is combined with the maximum tangential stress criterion to determine the crack propagation angle. An analytical method based on Neuber’s procedure has been developed. The method provides the values of the microstructural support factor as a function of the mode ratio and the notch opening angle. The support factor is considered to be independent of the microstructural support length. Finally, for comparison, the support factor is determined on a purely numerical basis by iterative analysis of finite element models. The present paper is aimed to give a brief overview of the recent findings on this challenging topic making clear the state of the art.

Crack initiation at V-notch tip subjected to in-plane mixed mode loading: An application of the fictitious notch rounding concept

The fictitious notch rounding concept is applied for the first time to V-notches with root hole subjected to in-plane mixed mode loading. Out-of-bisector crack propagation is taken into account. The fictitious notch radius is determined as a function of the real notch radius?? the microstructural support length and the notch opening angle. Due to the complexity of the problem, a method based on the simple normal stress failure criterion has been used. It is combined with the maximum tangential stress criterion to determine the crack propagation angle. An analytical method based on Neuber's procedure has been developed. The method provides the values of the microstructural support factor as a function of the mode ratio and the notch opening angle. The support factor is considered to be independent of the microstructural support length. Finally, for comparison, the support factor is determined on a purely numerical basis by iterative analysis of FE models.

V-notches subjected to combined tension and torsion loadings: the application of the fictitious notch rounding concept

The fictitious notch rounding concept is applied for the first time to V-notches subjected to combined modes I and III loading. The fictitious notch radius is determined as a function of the real notch radius, the microstructural support length and the notch opening angle. Due to the complexity of the problem, a method based on the simple normal stress failure criterion has been employed in the present contribution. An analytical method based on the original Neuber’s procedure has been developed. The method provides the values of the microstructural support factor as a function of the mode mixity ratio and the notch opening angle. The support factor is considered to be independent of the microstructural support length. The determined support factors are validated by means of a purely numerical basis by means of a large bulk of FE models. Finally the criterion is applied to a set of data taken from the literature.

Fictitious notch rounding concept applied to V-notches with root hole subjected to in-plane mixed mode loading

The fictitious notch rounding concept is applied for the first time to V-notches with root hole subjected to in-plane mixed mode loading. Out-of-bisector crack propagation is taken into account. The fictitious notch radius is determined as a function of the real notch radius, the microstructural support length and the notch opening angle. Due to the complexity of the problem, a method based on the simple normal stress failure criterion has been used. It is combined with the maximum tangential stress criterion to determine the crack propagation angle. An analytical method based on Neuber’s procedure has been developed. The method provides the values of the microstructural support factor as a function of the mode ratio and the notch opening angle. The support factor is considered to be independent of the microstructural support length. Finally, for comparison, the support factor is determined on a purely numerical basis by iterative analysis of FE models.

Progressive damage and failure strength of notched woven fabric composites under axial loading with varying strain rates

This study investigated the failure of notched and un-notched plain weave composite specimens subjected to varying strain rate loading. Different strain rate axial loads were applied to observe the rate effect on the failure. Both uniform and non-uniform strain rate loads were applied to the notched and un-notched composite specimens, respectively. Notched specimens showed initial cracks at the edge of the hole before final fracture. The initial crack under tensile loading became smaller as the strain rate increased. The initial crack length was predicted using the finite element analysis of the non-homogeneous, micromechanics-based model. The predicted length agreed well with the experimental measurement. Application of the initial crack size for the characteristic distance of the Average Stress failure criterion yielded acceptable tensile notch strengths. The compressive notch strength was less sensitive to the tensile notch strength. The non-constant, varying strain rate loading showed that the failure strength and stiffness depend on the history of the applied loading rates. The effects of the varying strain rates on both notched and un-notched specimens were different qualitatively. However, the strength ratios of the notched to un-notched specimens under varying rates were greater than those under constant rates regardless of tensile or compressive loading.

Experimental and finite element analysis on the performance of vacuum-assisted resin infused single scarf repairs

The high quality composite components produced by the modern manufacturing techniques necessitate the evolvement of repair procedures that produce comparable, in terms of structural integrity, post-repaired components. The vacuum-assisted resin infusion processing method is essentially a modern composite fabrication process and it is currently adapted in the production line of many industries. The technique is considered in the current paper as a repair route where a scarf recess is used as a mould cavity. The effectiveness of the repair technique is evaluated by examining two configurations that are constructed under certain scarf patch design guidelines. The fabrication and quality control procedures of the vacuum-assisted resin infused repair patches are described and experimental tests are carried out to measure their performance. Finite element analysis of the repair configurations is performed, in order to analyze and compare the repair geometries selected. The critical stressed areas from the analyses are identified as potential fracture locations and the stress distributions are used to predict the strength of the repairs using the Tsai-Wu and average stress failure criterion (ASFC). The FE (finite element) results are found to be in good agreement with the experimental findings. The repairs present high strengths approaching that of the control specimens with neither of the configurations perpetuating failure cohesively within the bondline for the taper ratios examined, validating in that way the vacuum-assisted resin infusion repair methodology.

Application of genetic algorithm for optimum design of bolted composite lap joints

The genetic algorithm (GA), a powerful optimization technique for multiple extrema functions in multidimensional search spaces, is applied in conjunction with stress analysis to achieve optimum designs of bolted composite lap joints. The objective of the optimization is to ensure the highest strength of the joint. In this study, the laminate thickness, laminate lay-up, bolt location, bolt flexibility, and bolt size are considered as design variables. The contact stresses (bolt loads) are determined by a combined complex potential and variational formulation. In this formulation, the equilibrium equations are satisfied exactly and the boundary conditions are enforced by minimizing the total potential. The contact stresses as well as the contact region are determined through an iterative procedure as part of a solution method that accounts for the effects of finite geometry and by-pass loading. The fitness function for the GA optimization is based on the average stress failure criterion for predicting net-section, shear-out, and bearing failure modes in bolted lap joints.

Modelling of reinforced polymer composites subject to thermo-mechanical loading

A coupled finite element model is developed to analyse the thermo-mechanical behaviour of a widely used polymer composite panel subject to high temperatures at service conditions. Thermo-chemical and thermo-mechanical models of previous researchers have been extended to study the thermo-chemical decomposition, internal heat and mass transfer, deformation and the stress state of the material. The phenomena of heat and mass transfer and thermo-mechanical deformation are simulated using three sets of governing equations, i.e. energy, gas mass diffusion and deformation equations. These equations are then assembled into a coupled matrix equation using the Bubnov–Galerkin finite element formulation and then solved simultaneously at each time interval. An experimentally tested 1.09 cm thick glass-fibre woven-roving/polyester resin composite panel is analysed using the numerical model. Results are presented in the form of temperature, pore pressure, deformation, strain and stress profiles and discussed. The maximum normal stress failure criterion is used in order to establish the load-bearing capability of the composite panel. Significant pore gas pressure build-ups (to 0.8 MPa and higher) have been perceived at high thermo-chemical decomposition rates where the material experiences a complex expansion/contraction phenomenon. It is found that the composite panel experiences structural instability at elevated temperatures up to 300°C but retains its integrity even under moderate external loading. Copyright © 2005 John Wiley & Sons, Ltd.

Experimental and Analytical Studies On the Onset of Delamination in Laminated Composites

A large number of laminates prone to delamination under uniaxial loading have been tested. The onset of delamination is determined on the basis of acoustic emission data. A two parameter failure criterion, i.e. average interlaminar normal stress failure criterion on σ=, has been used in conjunction with the stress analysis done by applying the global local model [5]. A comparison between the experimental and the predicted edge delamination threshold strengths has been made. For the class of laminates studied, the onset of edge delamination load can be accurately predicted.

Effects of Holes on Graphite Cloth Epoxy Laminates Tension Strength

A series of tests was conducted on laminates made from a graphite cloth epoxy material and having circular machined holes. The tests showed room temperature behavior similar to holed tape laminates except that residual or notched-to-unnotched strength ratio of the cloth laminates were somewhat greater. Increasing temperature and degree of laminate orthotropy was demonstrated to increase the effective notch sensitivity to holes. Strain gages exhibited virtually linear response to failure except on or immediately adjacent to the hole edge, where significantly nonlinear response was evident well below the failure load. Highly localized anisotropic failures apparently are the cause of this behavior, suggesting it will be difficult to model analytically. Test results generally followed the trends predicted by the average stress failure criterion, but suggest the parameter a0 is a function of both temperature and layup. X-ray pictures of the failed specimens show that internal damage is restricted to a small distance from the failure surface.

Applications of the average stress failure criterion. Part II. Compression: Niusmer, R.J. Journal of Composite Materials, Vol 13 (January 1979) p 49

Applications of the average stress failure criterion. Part II. Compression: Niusmer, R.J. Journal of Composite Materials, Vol 13 (January 1979) p 49

Application of the average stress failure criterion. Part I: Nuismer, R.J. and Labor, J.D. Journal of Composite Materials Vol 12 (July 1978) pp 238–249

Application of the average stress failure criterion. Part I: Nuismer, R.J. and Labor, J.D. Journal of Composite Materials Vol 12 (July 1978) pp 238–249

Applications of the Average Stress Failure Criterion: Part II — Compression

Results are presented for the compressive fracture strength of several Gr/Ep (AS/3501-5) laminates containing countersunk holes with both loaded and unloaded fasteners in place. Finite element stress analyses are presented which approximate the countersink geometry and the elastic contact problem. The average stress failure criterion is successfully used to predict the observed strengths in all cases considered.

Applications of the Average Stress Failure Criterion: Part I — Tension

Results are presented for the fracture strengths of several Gr/Fp (AS/3501-5) laminates containing countersunk holes and normal and slant cracks. Countersinks are treated as effective uniform holes and slant cracks as effective normal cracks. It is shown that the average stress criterion leads to acceptable strength predictions for all cases considered.