Biaxial Stress Ratio Research Articles

Fatigue Degradation and Life Prediction of Glass Fabric Polymer Composite under Tension/Torsion Biaxial Loadings

Fatigue degradation and life prediction for a plain woven glass fabric reinforced polyester under tension/torsion biaxial loadings were investigated. Typical S-N diagrams were given at several biaxial ratios when the biaxial cyclic loads were proportionally applied to the specimens. A fatigue damage accumulation model based on the continuum damage mechanics theory was developed, where modulus decay ratios in tension and shear were used as indicators for damage variables D. In the model, the damage variables are considered to be second-order tensors. Then, the maximum principal damage variable, D* is introduced. According to the similarity to the principal stress, D* is obtained as the maximum eigenvalue of damage tensor [D']. Under proportional tension/torsion loadings, fatigue lives were satisfactorily predicted at any biaxial stress ratios using the present model in which the fatigue characteristics only under uniaxial tension and pure torsion loadings were needed. For a certain biaxial stress ratio, the effect of loading path on the fatigue strength was examined. The experimental result does not show a strong effect of loading path on the fatigue life.

Fatigue Life Prediction of Glass Fabric Polymer Composites under Tension-Torsion Biaxial Loadings.

Fatigue degradation and life prediction for a plain woven glass fabric reinforced polyester under tension-torsion biaxial loading were investigated. A fatigue damage accumulation model based on the continuum damage mechanics theory was developed, where modulus decay ratios in tension and shear were used as indicators of damage variables (D). In the model, the damage variables are considered to be second-order tensors. Then, the maximum principal damage variable, D* is introduced. According to the similarity to the principal maximum stress, D* is obtained as the maximum eigenvalue of damage tensor [D' ]. Under proportional tension-torsion loading, fatigue lives were satisfactorily predicted at any biaxial stress ratios using the present model in which the fatigue characteristics only under uniaxial tension and pure torsion loadings were required.

Fatigue Behavior of a Plain-Woven Glass Fabric Laminate under Tension/Torsion Biaxial Loading

Fatigue strength and stress-strain response of a plain-woven glass fabric laminate subjected to pulsating tension/pulsating torsion biaxial loading were investigated. Biaxial loads were proportionally applied. S-N curves at different biaxial stress ratios were obtained. For the S-N diagram, the normalized fatigue strength defined by the ratio between the cyclic biaxial stress and the static strength, was used. All data roughly locate on a slightly wide band on the normalized S-N diagram, although the tendency that the slope of the S-N curve becomes low with an increase of the shear stress component is distinguishable. Modulus decays both in tension and shear with respect to loading cycles under biaxial loading are almost the same as those under uniaxial tension and pure torsion loadings, respectively. The direction of matrix cracks is dependent on the principal stress direction under biaxial loading although it does not coincide with the direction of the principal plane.

Fatigue Damage Evaluation of a Circular Hole-Notched GFRP under Tension-Torsion Biaxial Loading. 1st Report, Fatigue Strength and Damage Process.

Fatigue strength and the failure process of a hole-notched glass FRP under tension-torsion biaxial cyclic loading were investigated in this paper. Thin cylindrical specimens were used. Fibers of the reinforcement (plain woven glass cloth) were aligned parallel to the longitudinal and circumferential axes of the specimen. The damage state at each biaxial stress ratio (α : the ratio of normal stress to shear stress) was observed macroscopically and microscopically. The experiments reveal the following results. The damage progression is dependent on the biaxial stress ratio. When α=1/0, damage spreads radially from the hole, but only covers an area of π/4 to either side of the circumferential axis, in both directions along the circumferential axis. When α=0/1, damage progresses radially along both longitudinal and circumferential axes. We call each of these a fatigue band. Under biaxial loading, macroscopic and microscopic damage states have both types of damage at α=1/0 and α=0/1.

Fatigue Behavior of Plain Woven Glass-Fabric Laminates under Tension/Torsion Combined Loading. Effect of Shear Stress and Cyclic Condition on Fatigue Failure.

Fatigue strength and stress-strain response of plain woven glass fabric laminates subjected to combined loadings with pulasating tension and alternate torsion were investigated in this study. To distinguish the difference of fatigue failure behavior between that under pulsating torsion loading and that under alternate torsion loading, the alternate torsion test was also conducted. Fatigue strength and stress-strain response under alternate torsion loading were compared with that under pulsating torsion loading. From the experiment, it is found that the normalized fatigue strength (which is cyclic biaxial stress divided by the static strength) under pulsating tension/alternate torsion combined loading is dependent on the biaxial stress ratio. The fatigue strength under alternate torsion loading is much lower than that under pulsating torsion loading. The stress-strain response also shows nonlinear behavior more strongly than that under pulsating torsion loading.

Morphological Aspects of Fatigue Crack Growth under Biaxial Loading Conditions

In order to investigate the fatigue crack growth behavior under various biaxial loading conditions, twelve pieces of welded fatigue test specimen are designed in such a manner that the repeated nominal biaxial stress range ratios vary from 0.2 to 2.0 at the orthogonal joint of the specimen. It is of great interest to understand the sharp crack turning under certain biaxial loading conditions, where a crack changes its propagating direction approximately perpendicular to the initial direction. Various morphological modes of fatigue failure are actually obtained by experiments in the present work.It is also important to estimate an accurate crack path by numerical simulation for the proper understandings of fatigue crack propagation behavior. A step-by-step finite element approach has been proposed for fatigue crack path prediction, in which a two-dimensional cracked domain is remeshed by the modified quadtree mesh generation algorithm, and the stress field ahead of the current crack tip is analyzed by taking account of the higher order stress field parameters. A curved crack increment can be determined by using the first order perturbation solution together with the local symmetry criterion. The crack tip extends for a certain increment size, and the procedure is repeated for the next step. The present method is applied to the simulations of the fatigue test specimens. It is found that the simulated crack paths are in fairly good agreement with the experimental results and that the curved paths of fatigue cracks could be greatly influenced by the biaxial stress ratios, the loadings, and the geometry of the stress concentration corner.Although fairly good agreements are obtained between the simulated crack growth lives and the experimentally obtained ones for simple three point bending specimens in a previous paper, significant discrepancies are sometimes observed in the present study. We have not had the definite answer to the question, but one of the sources of the disagreement could be the compressive welding residual stress in the test specimens, which could significantly reduce the effective stress intensity ranges of some specimens.

FATIGUE CRACK GROWTH UNDER BIAXIAL LOADING

Fatigue crack growth under biaxial loading for long cracks subjected to low cyclic stress levels was investigated. The biaxial stress ratio λ ranging from ‐0.5 to + 1.0 was considered. The strain energy density factor range was used as the criterion for predicting the crack growth rates and crack path. The agreement between prediction and experimental results was reasonable for crack growth rates and marginal for crack paths. The investigation highlighted the inherent difficulties for crack path prediction and indicated the increased sensitivity to initial crack angle and biaxial stress ratio when the biaxial stress ratio approaches unity.

Effect of Biaxial Stress on the Propagation of Mode I Small Surface Crack.

The crack propagation rate da/dN at the specimen surface or db/dN toward the inner direction perpendicular to the specimen surface and crack opening displacement COD of a mode I small surface crack in a round bar are examined under biaxial stresses by means of the combination of plane bending and cyclic torsion. When the stress intensity factor range ΔK* at the deepest point of the crack periphery is the same, db/dN increases with the decrease in biaxial stress ratio C. An analogous tendency is recognized in the relationship between da/dN and ΔK at the specimen surface. A unique relationship is obtained between da/dN and crack tip opening displacement CTOD in spite of C. Thus, it can be concluded that the main factor which controls da/dN is CTOD.

Measurement of Biaxial Stress by an Electrodeposited Copper Foil with a Microcircular Hole. 3rd Report. Adaptation to the Stress Concentrated Location under Biaxial Tension.

Although the copper electroplating method of stress analysis can only detect the shearing stress amplitude, microcircular holes made in electrodeposited copper foil enable separation and measurement of the first and second princical stresses with biaxial stress conditions of a negative biaxial stress ratio. In this paper, developing the above idea, a method of detecting both principal stresses at the stress-concentrated location with a positive biaxial stress ratio is presented. The accuracy of this method is ascertained by examining the stress state near the hole in a plate under uniaxial tension and that at the bottom of a chircular groove in a shaft under bending.

Some strength studies on FRP laminates

The usage of fibre reinforced plastics can lead to a significant reduction in the weight of structural elements. The most important design variables in laminate design are the fibre orientation angle, ply thickness and fibre volume fraction. The first ply failure strength for [0/90/ ± 45] s laminate with different material systems and the corresponding first ply failure envelopes are presented for different in-plane loading conditions and ply orientations. The optimum biaxial stress ratio gives the highest value of the major failure load. At equal biaxial loading, all the plies of the laminate fail simultaneously in tension as well as compression for all values of laminate orientation angle.

Fatigue Behavior of Plain Woven Glass Fiber Laminates under Pulsating Tension/Pulsating Torsion Combined Loading.

Fatigue Strength and stress-strain response of plain woven glass fibric laminates subjected to pulsating tension/pulsating torsion combined loading were studied in this paper. In order to evaluate the biaxial fatigue failure strength, the normalized fatigue strength that a cyclic biaxial stress is divided by the static strength was used in S-N curves. According to the test results, it is found that all data locate in a slightly wide band on the S-N plot in spite of different biaxial stress ratios, but the tendency that the slope of the S-N curve becomes low in case of a high shear stress component, can be distingushable. The tendency of modulus decays in both tension and shear even under combined loading is almost the same as those under uniaxial tension and pure torsion loadings, respectively. The direction of matrix cracking seems dependent on the principle stress direction under pulsating tension/pulsating torsion combined loading although it is also strongly influenced by fiber orientation.

Effect of Biaxial Stresses on the Threshold of Small Surface Crack Propagation.

In order to investigate the effect of biaxial stresses due to the combination of plane bending and cyclic torsion on the threshold of mode I small surface crack propagation, the relationship between the threshold stress and crack length under various biaxial stress ratios C was examined using a circular shaft made of carbon steel. The threshold stress intensity factor is constant above some crack length in each C, but becomes lower with the decrease in C. The length of the slipped regionγp at the crack tip on the threshold of crack propagation is nearly constant regardless of C. Therefore, if the threshold curve of crack propagation in C = 0 is determined experimentally, the threshold curves in other C can be deduced from the relationship betweenγp and C.

The Effect of Plate Thickness on the Propagation Behaviour of Mode I Surface Crack under Biaxial Btresses by the Combination of Plane Bending and Cyclic Torsion.

The effect of plate thickness on the propagation rate of a mode I surface crack under biaxial stresses by the simultaneous action of plane bending and cyclic torsion was examined, and the crack opening displacement COD was measured by magnifying a scanning electron micrograph 15000 times. The relationship between the propagation rate da/dN and the stress intensity factor rangeΔK depends on both the biaxial stress ratio C and the maximum principal stress amplitudeσ1. COD measured under the same conditions ofσ1 and crack length increases with the decrease in C. A unique relationship is obtained between da/dN and crack tip opening displacement CTOD, irrespective of C and σ1. Thus, it can be concluded that the main factor which controls da/dN is CTOD.

PTFEコーテッド・ガラス繊維布(膜材料A種)の非線形伸長曲線への多段線形近似とその応用

The highly nonlinear extension curves of a PTFE-coated plain-weave glass fiber fabric were measured under three cases of biaxial stress ratio condition. A 4-step-linear approximation which uses least square method was applied on the extension curves. Then the elastic parameters were determined for each of the approximated 4-step-lines, and the 4-step-lines tracked on the measured curves satisfactorily. Further, using the elastic parameters, the deflection of a rectangular flat specimen (40×30 cm) subjected to pressure was analyzed.

The Propagation Behaviour of Mode I Surface Cracks under Biaxial Stresses by the Combination of Plane Bending and Cyclic Torsion

Crack propagation rate of a model surface crack in a plate, the crack tip opening stresses or displacements under various biaxial stress ratios by the simultaneous action of plane bending and cyclic torsion are examined. The aspect ratio of a crack is not affected by the biaxial stress ratio but the relationship between the propagation rate da/dN and the stress intensity factor range ΔK or the effective stress intensity factor range Δ Keff depends on it. This is mainly due to the differences of both CTOD and the scale of the slipped region at the crack tip caused by the difference of biaxial stress ratio.

On Fatigue Crack Paths under Biaxial Loading Conditions

Considering welded thin plate structures such as ships, which are orthogonally stiffened by periodically arranged transverse and longitudinal frames, attentions should be focused to the fatigue strength at the orthogonal intersections of frames where severe stress concentration may occur due to the structural discontinuity and weldment. Stress states of frames at intersections are generally biaxial, because loads transmitted from the intersected members act perpendicularly to the frame direction. The biaxial stress ratio varies depending on the load effects of frames such as axial stress due to hull girder bending and local bending stress due to lateral pressure acting on shell plating.Formerly fatigue damage was observed around slots and web stiffeners of transverse girders. In order to prevent this type of fatigue damage, a lot of efforts had been made so that the certain refinement of structural details were accomplished. Recently, new type of fatigue damage is observed in longitudinals, where fatigue cracks extend toward shell plating. The change of the fracture modes may be caused by the change of the proportion of transeverse and longitudinal stresses, which is closely related to the biaxial stress ratio of the intersection.In the present paper an analysis model is introduced in order to investigate paths of fatigue cracks propagating under various biaxial stress conditions. The local symmetry criterion, which was proposed by Kitagawa et al. and confirmed by experiments for paths of fatigue crack growth, is applied to the computational crack path prediction. In order to avoid the complexities due to nonproportional loading, numerical simulations are performed for the purely in phase or out of phase biaxial stress conditions. Considering a fatigue crack whose growth length is within three to five times of the initial crack length, it extends approximately normal to the larger stress direction except that the biaxial stress ratio is close to unity.

THERMAL FATIGUE UNDER MULTIAXIAL STRESSES

AbstractThermal fatigue under multiaxial stresses has been investigated. Circular cylindrical specimens were tested under thermal fatigue which was in‐phase with axial mechanical fatigue loading. The axial forces on the specimens were varied throughout the test programme, but all the temperature cycles were identical, so various biaxial stress and strain ratios were obtained. Straight thermal fatigue cracks occurred in different directions and also net‐like crazes in various patterns were observed on the surfaces of the specimens. The transient temperature, stress and strain fields have been calculated with a thermal elasto‐plastic Finite Element Method. Comparing test results with calculations, it appears that the patterns of thermal fatigue cracks are dependent on the stress state and the plastic strain state, not on the strain state. The direction of cracks is perpendicular to the maximum principal stress and the maximum plastic strain. Net‐like thermal fatigue crazes will occur when one principal stress is about the same as the other one and one plastic strain component is approximately equal to another.

The propagation behaviour of mode I surface cracks under biaxial stresses by the combination of plane bending and cyclic torsion.

Crack propagation rate of a model surface crack in a plate, the crack tip opening stresses or displacements under various biaxial stress ratios by the simultaneous action of plane bending and cyclic torsion are examined. The aspect ratio of a crack is not affected by the biaxial stress ratio but the relationship between the propagation rate da/dN and the stress intensity factor range ΔK or the effective stress intensity factor range Δ Keff depends on it. This is mainly due to the differences of both CTOD and the scale of the slipped region at the crack tip caused by the difference of biaxial stress ratio.

Development of crystalline structure during tubular film blowing of low‐density polyethylene

AbstractDevelopment of crystalline structure during the tubular film blowing of low‐density polyethylene was investigated, using wide‐angle X‐ray diffraction technique, low‐angle light scattering, and scanning electron microscopy. In the study, commercial grades of both high‐pressure low‐density polyethylene (HP‐LDPE) and low‐pressure low‐density polyethylene (LP‐LDPE) (also, commonly referred to as linear low‐density polyethylene, LLDPE) were used. The applied stresses at the freeze line were determined using theoretical expressions derived in an earlier publication [C. D. Han and T. H. Kwack, J. Appl. Polym. Sci., 28, 3399 (1983)]. The applied stresses, S11F and S33F, at and above the freeze line in the machine and transverse directions were expressed in terms of the tension at the take‐up device, take‐up ratio, blow‐up ratio, and the pressure difference across the film of the bubble. These applied stresses were used to interpret the crystalline axes' orientation in the tubular blown films. It was found that the magnitude of S11F is an important process parameter for the crystalline axes' orientation and that the biaxial stress ratio (S11F/S33F) appears to be a determining factor in the distribution of fibrillous nuclei and crystalline texture, as well as film anisotropy.

Dynamic crack curving and branching under biaxial loading

A 16-spark-gap camera was used to record the dynamic photoelastic patterns of ten centrally cracked, Homalite-100 specimens which fractured under ten initial biaxial-stress ratios ranging from 3.7 to 0, some of which do not exist in normal fracture specimens. The dynamic photoelastic patterns of curved cracks were used to verify the previously developed dynamic-crack-curving criterion. Cracks which immediately curved upon propagation in three specimens under abnormally high inital biaxial loading were used to verify the static counterpart of the dynamic-crack-curving criterion under these extreme loading conditions. A previously developed dynamic-crack-branching criterion was also verified by four dynamic photoelastic results involving cracks which eventually branched under the lower initial biaxial loading.