Prediction Of Notched Strength Research Articles

Anisotropic size effect law for notched strength of unidirectional carbon/epoxy laminates – Part 1: Formulation

A multiaxial quasi-brittle failure criterion for notched orthotropic composites is developed with an emphasis on establishment of an analytical formula to predict their anisotropic notched strength for any notch size under any multiaxial proportional loading. It is formulated by replacing the principal unnotched strengths with the principal notched strengths in the framework of the Tsai–Hill static failure criterion for orthotropic composites. The effects of notch size and specimen width on the principal notched strengths are described by means of the Suo-Ho-Gong model that can consider notch ductile-to-brittle transition. From the proposed multiaxial quasi-brittle failure criterion, an analytical formula is derived to predict the notched strength of finite orthotropic composite plates under multiaxial proportional loading at any angle with the principal directions of material anisotropy. The notched strength prediction formula involves a generalized notch sensitivity parameter that can be defined for any multiaxial state of stress. The multiaxial notch sensitivity parameter allows uniquely defining an intrinsic equivalent mode-I fracture toughness that is independent of notch size as well as of specimen width for any multiaxial proportional loading. Furthermore, an anisotropic size effect law for apparent equivalent mode-I fracture toughness that considers not only the effect of notch size but also the effect of specimen width is derived from the failure criterion. Finally, a quasi-brittle failure criterion for notched interface is briefly discussed as a particular case of the proposed quasi-brittle failure criterion for notched orthotropic composites.

Notched strength prediction of glass fiber reinforced composite based on fracture toughness analysis

The notched strength prediction of normal glass mat composite and needle punched glass mat composite based on fracture mechanics was carried out in this study. The prediction constitutes of three parts including establishing the relation between characteristic distance and notch strength ratio (a ratio of notch strength to unnotched strength), modulus calculation in thickness direction and fracture toughness measurement. The characteristic distance was determined by point stress criterion and calculated from finite element analysis. After contrastive analysis from a mass of tensile results on notched specimens with an open hole, a relation between characteristic distance and notch sensitivity was established. Modulus calculation was calculated according to the classic theory of “Rule of Mixtures” and “Reuss Model”. After that, the results of modulus calculation together with fracture toughness results were employed to establish the relation between notch strength and characteristic distance according to elastic fracture mechanics. The characteristic distance was used in this part as a parameter of a crack. Finally, from the two equations between notch strength and characteristic distance, the notched strength of composite with an open hole can be predicted. The predicting results were compared and analyzed with experiment results.

Notched Strength Prediction and Verification of APC-2 Composite Laminates at Elevated Temperature

The notched strength of AS-4/PEEK (APC-2) composite laminates with a central hole at elevated temperature was systematically studied by both analytical and empirical methods. First, the APC-2 cross-ply [0/90]4s panels were fabricated and cut into samples. Each sample was drilled a hole in the center with five kinds of diameters, such as d=0(unnotched), 1, 2, 3, and 4mm. Then, the samples were subjected to quasi-static tensile tests at elevated temperatures, including 25°C (RT), 75, 100, 125, 150 and 175°C, to measure their mechanical properties. The average values of received notched strength were affected significantly by stress concentration and high temperature. In analysis the prediction of residual strength by point stress criterion (PSC) was adopted first and found unsatisfactory due to at least 15% errors with experimental data. Then, the modified PSC was used with the varied characteristic length dependent on nature of material and specimen geometry. The predicted notched strengths by the modified PSC model were in very good agreement with experimental data. The predictive results were not only precisely validated, but extended to the application at elevated temperature.

Generation and validation of failure assessment diagram for notched strength prediction of solid propellant tensile specimens

Failure assessment diagrams are generated utilising the well known inherent flaw model and stress fracture models for accurate prediction of notched tensile strength of different cracked configurations of a solid propellant material. The notched strength estimates from the fracture models are found to be close to the test results. This study indicates that any one of the above fracture models may be used for the generation of a failure assessment diagram used to predict the notched strength of cracked configurations made of solid propellant materials.

An Improved Cohesive Zone Model for Residual Notched Strength Prediction of Composite Laminates with Different Orthotropic Lay-Ups

The traditional methods employing a characteristic length approach to predict residual strength of notched laminates did not recognize damage development prior to final failure. Due to this lack of physical basis, re-calibration is often needed when the specimen geometry and size are changed. More recent models such as the Damage Zone Model (DZM), Cohesive Zone Model (CZM) and the Effective Crack Growth Model (ECGM), have recognized the occurrence of progressive material softening ahead of the notch tip prior to catastrophic failure. However, since the anisotropic characteristic of the composite laminate has not been properly accounted for, these models may not be widely applicable for the laminates with different degrees of anisotropy. In this study, an Improved Cohesive Zone Model (ICZM) with proper consideration for anisotropy is proposed to predict the notched strength of composite laminate. Based on three fundamental parameters: namely the unnotched strength 0, the apparent fracture energy Gc and the effective longitudinal stiffness E0, this model successfully predicted the strength of notched composite laminates with various degrees of anisotropy. The current model also gives accurate prediction of the progressive damage zone size in quasi-isotropic and cross-ply laminates.

A physically-based model for the notched strength of woven quasi-isotropic CFRP laminates

Damage growth and fracture at circular holes in quasi-isotropic CFRP laminates loaded in tension has been studied. The laminates were based on two weave types and of three different thicknesses. A notch edge damage analysis was performed on a layer by layer basis after decomposition of the matrix. It was shown that near the notch edge, damage in the form of fibre tow failure occurred in the tows orientated at 0°, whilst the tows oriented at 45° within the damage area remained intact to loads just below the maximum load. The well known semi-empirical point and average stress criteria resulted in accurate notched strength predictions with the average stress criterion being better than the point stress criterion. A recently developed critical damage growth model, requiring as input parameters the unnotched strength and fracture toughness of the laminate which were measured from independent experiments, yielded accurate notched strength predictions, while being easy to implement. The resilience of the critical damage growth model was investigated and it was found that a variation in both the input parameters of the model by 10% result, even in the worst case, in a 10% variation in the notched strength predicted by the model.

Notched strength prediction of laminated composite under tensile loading

A modified point stress criterion for predicting the notched strength of glass fibre and carbon fibre laminated composites containing through the thickness centrally located circular or elliptical hole or a centre crack is presented here. The effects of hole size and specimen width on the fracture behaviour of several woven fabric composite plates are also studied. The results show that the point stress criterion the characteristic length ( d 0) depends on the hole size as well as width of the plate. The analytical results are in good agreement with the existing test model results.

Characterisation and modelling of the notched tensile fracture of woven quasi-isotropic GFRP laminates

Damage growth and fracture at circular holes in quasi-isotropic laminates, assembled from four layers of woven glass fabric, loaded in tension has been studied. A comprehensive notch-edge damage analysis was performed by a combination of recording tests on video, plan-view photography and a de-ply technique, enabling a layer-by-layer analysis. It was shown that the notch-edge damage initiation and propagation comprised matrix cracking, fracture of the 0° tows, delamination and longitudinal splitting. The tows in the fabric layers oriented at 45° within the damage zone remained intact up to the maximum load in a tensile test. The well-known semi-empirical point-stress and average-stress criteria resulted in accurate notched strength predictions with the average-stress criterion being better than the point-stress criterion. A recently developed critical damage growth model, requiring as input parameters the unnotched strength and fracture toughness of the laminate which were measured from independent experiments, yielded accurate notched strength predictions (to better than 10%), while being very easy to implement. Predicted damage zone lengths from the critical damage growth model generally agreed well with experimental observations.

Notched strength prediction of centre-hole carbon/carbon composites

The present work investigates the behaviour of 2D carbon/carbon (C/C) composites containing centre holes and proposes methodologies for the prediction of the residual strength of such C/C laminates. Two different concepts were adopted in order to understand the fracture behaviour of C/C composites in the presence of holes and to evaluate their strength. The first approach is based on the hypothesis of the existence of a damage zone around the hole, which originates during tensile loading. The second uses monitoring of the acoustic emission (AE) activity of the centre-hole specimen, loaded up to a stress level well below its failure strength, as an indication of damage formation, and combines it with a defined calibration curve. Both models predict very accurately the strength of notched laminates for a number of specimens tested.

Notched Strength Prediction of Holed Woven Glass/Epoxy Laminates with Tan's Models

The point strength model and the minimal strength model proposed by Tan were applied to predict the notched strength of three woven Glass/Epoxy laminates (two orthotropic and one quasi-isotropic) under monotonic uniaxial loading. In the two models, the stress field around the hole for a finite-width notched laminate was expressed by a numerical solution which was determined essentially by the characteristic roots of the notched laminate, and was anew determined in each rigidity degradation step because the rigidity and compliance matrices of the laminate (which give the coefficients in the characteristic equation) vary with the loading due to damages. The characteristic dimensions defined and adopted in the two models were also anew determined in each critical ply. The results show that the strength reduction factor (SRF) curves as a function of hole diameters determined with the characteristic dimensions of the ± 45 ° plies for the laminates studied can give much better notched-strength prediction results than with those of the 900 plies especially for the orthotropic laminates. The damage mechanisms in the woven laminates are very different from those in non-woven laminates.

Modified Tan's models for the strength prediction of woven laminates with circular holes

In order to study the strengths and damage mechanisms of three notched woven laminates (two orthotropic and one quasi-isotropic) under monotonic uniaxial loadings, two Tan's models were modified by introducing a numerical stress field around a hole in the laminate, recalculating both the local and global stress distributions, and determining the characteristic dimensions of every critical ply with progressive rigidity degradations. The results show that the strength reduction factor (SRF) curves as a function of hole diameter determined with the characteristic dimensions of the plies at ±45° can give much better notched strength predictions than those with the plies at 90°, especially for orthotropic laminates and where the damage mechanisms in woven laminates are very different from those in non-woven laminates.

Influence of finite width on notched laminate strength predictions

Notched strength of composite laminates is commonly predicted by first determining the stress distribution within the laminate and subsequent application of a stress fracture criterion. Common test specimen geometries typically require finite width stress distributions for correct data reduction and strength predictions. Numerical difficulties are encountered with this approach, however, because closed-form expressions for the stress distribution in orthotropic materials exist only for infinite width-to-hole diameter (w/D) geometries. In this paper, finite element stress analysis is presented for isotropic and orthotropic plates containing circular notches. Results are correlated with available analytical solutions. For geometries where w/D < 4 there is a substantial change in the normal stress distribution and related strength predictions. An approximate finite width stress distribution for orthotropic plates with circular notches is proposed and the influence of finite width on notched strength predictions is discussed.

Notched Strength Prediction and Design of Laminated Composites Under In-Plane Loadings

Two models based on the first-ply-failure stresses of notched and unnotched laminates are developed for the strength prediction of composite laminates containing an opening under in-plane loadings. Comparisons show that these models provide good agreement with experimental data for quasi-isotropic and orthotropic laminates containing a circular hole or a center crack. In conjunction with these models, a ranking method is applied for the laminate designs that is found reliable and very useful.

The prediction of R-curves and notched tensile strength for composite laminates

A new model is proposed to explain the cracking and fracture of notched composite laminates. It is based on the energy absorption associated with the micromechanisms of fracture. Crack-growth resistance curves (R-curves) are predicted for a wide range of laminate constructions and materials, and the corresponding notched strengths deduced. Both R-curve and notched strength predictions are in good agreement with published data. The effect of improved fibre-matrix bonding on laminate notched strength is investigated in a case-study, and is successfully predicted using the model.