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

Abstract

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.     

Modification of Dugdale model to include the work hardening and in- and out-of-plane constraints

In the paper the classical Dugdale model has been generalized taking into account the influence of the specimen thickness, in-plane constraint as well as the effect of the strain hardening on the level of stress distribution within the strip yield zone (SYZ). Modification has been performed utilizing Huber, Mises, Hencky as well as Tresca yield hypotheses and Guo Wanlin Tz coefficient. Results are presented in a form useful for applications. As an example, the modified model has been applied to draw the failure assessment diagram (FAD). New FAD’s have been compared with others adopted from the SINTAP procedures.     

A new approach to the positive mean stress diagram in mechanical design

The Gerber, modified Goodman, Soderberg, Bagci, ASME‐elliptic and Clemson diagrams are proposed for estimating mechanical element fatigue strength under positive mean and alternating stresses. However, all of these diagrams are either conservative or have fields containing stress greater than yield strength of mechanical element materials. The aim of this study was to propose a new simple diagram with an exponential power k for various types of mechanical element materials. Exponential power k values of steel and Al‐alloy materials were about 0.80 and 0.45, respectively. The proposed diagram (Sekercioglu line) had a minimum average absolute deviation (X_m) of 8.56 %, lower than the Bagci, ASME‐elliptic and Clemson diagrams. The Sekercioglu line can be successfully used in fatigue design processes because of its simple structure and its less conservative nature.     

Predicting fatigue S-N (stress-number of cycles to fail) behavior of reinforced plastics using fracture mechanics theory

The present study describes a model to predict fatigue S-N behavior, and thus fatigue life, of glass fiber reinforced thermoplastics by using a fracture mechanics approach. The model assumes the presence of an inherent initial flaw in the molded plastic parts and thus ignores crack initiation contributions. In this paper we describe how fatigue crack propagation rate data were obtained for the same three glass fiber reinforced plastics whose S-N behavior was previously described in detail. Using the measured constants from the crack growth data, and corresponding S-N data for uncracked specimens, the validity of the single initial flaw hypothesis was evaluated. From the analyzed results it is concluded that accurate S-N predictions are possible using this simple fracture mechanics model for some materials. The best results are obtained for glass filled polyamide, PA (nylon 66) and polycarbonate, PC; however, with polybutylene terephthalate, PBT, predictions were poor. It is also shown that S-N data for different glass fiber orientations can be predicted by combining the single flaw model with predicted fatigue crack propagation rate measurements. The latter are calculated from a generalized crack growth rate expression utilizing the strain energy release rate fracture mechanics parameter, which was previously described.     

Failure of amorphous polystyrene

The failure behaviour of amorphous polystyrene was studied in methanol and ambient air under constant load and strain rate conditions. The good correlation found between fracture mechanics theory and the test results of both crazing and fracture indicates that fracture mechanics theory can be used in predicting failure of amorphous polystyrene. From the fracture mechanics analysis of the results it is inferred that the kinetics associated with craze initiation and crack propagation are similar and that the inherent flaw responsible for failure first initiates the craze in which a crack is then formed. Both the distribution of inherent flaws and the kinetics of crazing and fracture are dependent on the test environment.     

Variable amplitude fatigue of autofrettaged diesel injection parts

Experimental and analytical investigations of constant and variable amplitude fatigue life of not autofrettaged and autofrettaged components have been performed. In variable amplitude loading the new standardised CO mmon‐ RA il‐ L oad sequence CORAL has been used as well as two‐level‐tests with small cycles at high mean stresses interrupted by large cycles for the evaluation of load sequence effects. The results of the two level tests show that small cycles with amplitudes far below the fatigue limit cause fatigue damage. Life calculations have been performed according to the nominal stress approach with S‐N‐curves and improved Miner’s Rule, linear‐elastic fracture mechanics with 3D‐weight functions, elastic‐plastic fracture mechanics applying an extended strip yield‐model, and explicit 3D‐FE‐simulation of fatigue crack growth with predefined crack fronts. All approaches are appropriate for predicting realistic variable amplitude lives. From a practical point of view the explicit 3D‐FE‐simulation of fatigue crack growth is too time‐consuming. However, such simulations show that the approaches based on linear‐elastic fracture mechanics and elastic‐plastic fracture mechanics with extended strip yield‐model capture the essential physics of fatigue crack growth in a realistic way.     

Phase diagrams beyond the critical point

Following a path in the usual p‐T‐diagrams of one‐component systems via the supercritical region it seems that one can make a transition from the liquid to the gas phase (and in reverse) without traversing a phase boundary curve, whereas in the sub‐critical region one clearly has to pass a phase boundary curve. To solve this paradox situation, the phase diagrams of one‐component systems are analyzed with respect to the phase transition from the liquid to the gas state in the sub‐ and supercritical range. It is shown that the critical point is not an isolated point or an end point on the phase boundary curve between the gaseous and the liquid phase in a p‐T‐diagram. Instead, it marks on the boundary curve just the transition between the section of a first order phase transition in the sub‐critical range and the section of a second or higher order phase transition in the supercritical range. Thus, the present phase diagrams of one‐component systems are incomplete with respect to the phase boundary curve between liquid and gas in the supercritical region. The result is illustrated using the model of a van der Waals gas.     

Mechanical properties of rock specimens containing pre‐existing flaws with 3D printed materials

Three‐dimensional printing (3DP) technology has undergone a rapid development in the last few years and become a useful tool in many research fields. This study applied 3DP technology to prepare solid specimens simulating rock‐type materials combined with computed tomography scanning and 3D image processing. 3DP specimens with pre‐existing flaws in different inclination angles were fabricated and then conducted a series of mechanical experiments to study the influence of number and inclination angle of pre‐existing flaw on strength and failure patterns under uniaxial compression. The experimental results indicated that 3DP specimens had similar mechanical properties with rock‐type materials. The 3DP specimens with 2 pre‐existing flaws had lower compressive strength with an average of 4.26 MPa, whereas compressive strength of specimens with one flaw was no less than 5.08 MPa. Different inclination angles led to various failure patterns and compressive strengths, which took on a V‐shaped curve with the increase of inclination angles. This study demonstrated that 3DP technology provided a new perspective for conducting laboratory experimental research of rock mechanics.     

Fracture mechanics modelling of constant and variable amplitude fatigue behaviour of field corroded 7075‐T6511 aluminium

For ageing airframe structures, a critical challenge for next generation linear elastic fracture mechanics (LEFM) modelling is to predict the effect of corrosion damage on the remaining fatigue life and structural integrity of components. This effort aims to extend a previously developed LEFM modelling approach to field corroded specimens and variable amplitude loading. Iterations of LEFM modelling were performed with different initial flaw sizes and crack growth rate laws and compared to detailed experimental measurements of crack formation and small crack growth. Conservative LEFM‐based lifetime predictions of corroded components were achieved using a corrosion modified‐equivalent initial flaw size along with crack growth rates from a constant K_max‐decreasing ΔK protocol. The source of the error in each of the LEFM iterations is critiqued to identify the bounds for engineering application.     

Local fracture criterion to describe failure assessment diagrams for a body with a crack/notch

The cohesive zone model and the criterion of average stress in the cohesive zone ahead of the crack/notch tip are used to describe failure assessment diagrams for cracked and notched bodies. The type of loading as well as the elastic stress concentration factor can significantly change the character of the failure assessment diagram.     

Effects of Shear‐Transverse Coupling and Plasticity in the Formulation of an Elementary Ply Composites Damage Model,Part I: Model Formulation and Validation

Abstract: Continuum damage mechanics (CDM) models have been employed successfully in the literature to predict the response of laminated composite materials. Some sophisticated models can include the effects of non‐linear shear and transverse damage progression, plasticity and shear‐transverse damage coupling. However, these models require non‐standard test data for calibration that may not always be available to a modeller. In this two‐part study, we examine the effect of neglecting plasticity parameters, and also the effect of neglecting both plasticity and shear‐transverse coupling parameters in simplified CDM models for predicting monotonic tensile strength. In part I, we develop simplified versions of the CDM model and test their ability to accurately predict the failure response of angle‐ply laminates. In part II, we provide details of the experimental test series carried out to determine the input parameters for the models. It was found that neglecting plasticity requires some approximations in the damage development laws, but the resulting model can predict well the response of the angle‐ply laminates tested under monotonic loading to failure. Neglecting shear‐transverse coupling is acceptable for the some materials.     

Fatigue life analysis of fiber reinforced concrete with a fracture mechanics based model

Fatigue life of fiber reinforced concrete (FRC) is theoretically analyzed with a fracture mechanics based model. The model accounts for the effect of cycle-dependent crack bridging properties in FRCs and predicts the number of cycles to failure defined by final fracture subsequent to stable fatigue crack growth in Mode I. The resulting theoretical S–N diagram was compared with experimental data reported in literature. The general agreement supports the validity of the current model, and reveals that cycle-dependent degradation of crack bridging controls fatigue life of FRCs. S–N diagrams are essential for material evaluation and structural design, and the model establishes the link between material structure and S–N diagram in an explicit manner, while the conventional stress-life approach realizes the link in an empirical manner.     

The use of constraint-modified failure assessment lines in failure assessment diagrams

Two possible methods of including the effect of constraint in a failure assessment diagram (FAD) of the R6 type are to change the definition of the quantity K_r(the ratio of the operative crack driving force to the current material toughness) or to modify the failure assessment line (FAL). An analysis of the relation between the treatment of ductile tearing using the FAD and the R-curve diagram, extended recently to include constraint effects in modified diagrams of the first type is shown here also to hold for the second. Provided that the projected growth path image (PGPI) is used to specify the motion of the assessment point during crack growth there is a complete correspondence of R-curve analysis with either type of FAD. The two methods, both formulated for any number of generic constraint parameters, are compared using a simple illustrative example in which the constraint is parametrized by T. The methods previously discussed for testing the consistency or conservatism of an engineering FAD can be extended to both types of generalized diagram which allow for crack tip constraint.     

An examination of the role of flaw size and material toughness in the brittle fracture of polyethylene pipes

At low temperatures and hoop stresses, polyethylene pipes fail by the time-dependent propagation of a crack. These brittle, fissure-like failures have been observed to initiate from adventitious flaws, and the concepts and methods of fracture mechanics indicate that flaw size should determine stress rupture lifetime. A number of controlled model experiments have therefore been undertaken to assess the influence of flaw size and material toughness on the stress rupture lifetimes of polyethylene pipes. To two different pipe grade polyethylene resins (one shorter, one longer lifetime resin) flaws of varying sizes have been added. For the shorter lifetime resin small flaws were, in addition, purposely excluded by the use of fine melt filtration techniques. Pipes containing added flaws or pipes where flaws were excluded were then stress rupture tested under those conditions designed to induce brittle failure by slow crack growth. The stress rupture lifetimes of the various pipes are then correlated with flaw size. The results of the tests using the shorter lifetime resin show that flaw size does have a significant influence. It is particularly interesting to note that melt filtration, which removes large inherent flaws, substantially improved the stress rupture lifetime. With respect to material toughness, the longer lifetime pipe grade polyethylene resin showed a healthy tolerance to included flaws. In respect of the stress rupture test preferred resins can therefore be identified in terms of their tolerance to included flaws.     

Automatic identification of functional kinematic bone features from MRT segmentation for gait analysis

We present a method for the segmentation of human leg bones and extraction of functional parameters of the femur using MRT images. The novelty consists in the use of dynamic models which will be adapted to the images of individual patients both globally to a whole leg bone and locally to individual parts of a bone. Thresholding and region growing procedures are applied for pre‐processing the images. For some parts of bones, for example the femur ball, we use a three dimensional VRML‐based (Virtual Reality Modelling Language) femur model as a reference in order to make the segmentation method more robust. Based on the segmentation and the 3D VRML model, we can extract functional (biomechanical) femur parameters which are needed for gait analysis.     

Modelling of paste flows subject to liquid phase migration

Particulate pastes undergoing extrusion can exhibit differential velocities between the solid and liquid phases, termed liquid phase migration (LPM). This is observed experimentally but understanding and predictive capacity for paste and extruder design is limited. Most models for LPM feature one‐dimensional analyses. Here, a two‐dimensional finite element model based on soil mechanics approaches (modified Cam‐Clay) was developed where the liquid and the solids skeleton are treated separately. Adaptive remeshing routines were developed to overcome the significant mesh distortion arising from the large strains inherent in extrusion. Material data to evaluate the model's behaviour were taken from the literature. The predictive capacity of the model is evaluated for different ram velocities and die entry angles (smooth walls). Results are compared with experimental findings in the literature and good qualitative agreement is found. Key results are plots of pressure contributions and extrudate liquid fraction against ram displacement, and maps of permeability, liquid velocity and voids ratio. Pore liquid pressure always dominates extrusion pressure. The relationship between extrusion geometry, ram speed and LPM is complex. Overall, for a given geometry, higher ram speeds give less migration. Pastes flowing into conical entry dies give different voids ratio distributions and do not feature static zones. Copyright © 2007 John Wiley & Sons, Ltd.