Biaxial Ratio Research Articles

Fatigue behavior of filament‐wound glass fiber reinforced epoxy composite tubes under tension/torsion biaxial loading

AbstractA study of filament‐wound glass fiber/epoxy composite tubes under biaxial fatigue loading is presented. The focus is placed on fatigue lives of tubular specimens under tension/torsion biaxial loading at low cycle up to 100,000 cycles. Filament‐wound glass‐fiber/epoxy tubular specimens with three different lay‐up configurations, namely [±35°]n, [±55°]n, and [±70°]n lay‐ups, are subjected to in‐phase proportional biaxial cyclic loading conditions. The effects of winding angle and biaxiality ratio on the multiaxial fatigue performance of composites are discussed. Specimens are also tested under two cyclic stress ratio: R = 0 and R = −1. The experimental results reveal that both tensile and compressive loading have an influence on the multiaxial fatigue strength, especially for [±35°]n specimens. A damage model proposed in the literature is applied to predict multiaxial fatigue life of filament‐wound composites and the predictions are compared with the experimental results. It is shown that the model is unsuitable for describing the multiaxial fatigue life under different cyclic stress ratios. POLYM. COMPOS. 28:116–123, 2007. © 2007 Society of Plastics Engineers

Crack paths and the problem of global directional stability

Crack paths of original Griffith crack and edge crack under biaxial remote mode-I loading after different local disturbances are calculated by using integro-differential equations of first-order perturbation and numerical simulation with FEM respectively. Considering the asymptotic behaviour for large crack lengths the problem of global directional stability is reinvestigated extending the work by Melin. For the Griffith crack, correct power functions for the asymptotic path with one or both crack tips growing have been determined. The well- known critical stress biaxiality ratio R c = 1 for the global directional stability has been obtained independently whether the crack is disturbed by local imperfections in geometry or in loading. For an edge crack the calculated critical stress biaxiality ratio for the global directional stability R c = 0.616, also irrespective of the local disturbances, corresponds to a positive T-stress and is considerably smaller than the value R > 0.95 estimated by Melin (2002). In general, cracks need not propagate asymptotically in the direction perpendicular to the largest principal stress (without crack). This is found to be due to the effect of the boundaries. Considering the initial crack growth exclusively, it is shown that the solution for crack path prediction in series expansion form as derived by Cotterell and Rice (1980) for traction-free crack faces (after correction of a misprint) is exact in the two first terms in all cases. Thus, for small crack growth the Cotterell and Rice solution is universal with respect to all loading and geometrical situations.

Fatigue Crack Propagation of Magnesium Alloy and Aluminum Alloy in Biaxial Stress Fields

In this research, fatigue crack propagation tests of magnesium alloy AZ31B and aluminum alloy 2024T3 were conducted under conditions of biaxial and uniaxial loading by using a cruciform specimen in a biaxial fatigue machine, in order to investigate the effect of non-singular stress cycling. From these comprehensive experiments, in the magnesium alloy, the remarkable effect was found in the specific biaxial load stress ratio RB (= σx 0/σy 0) on KI-da/dN relation. On the other hand, in the aluminum alloy, it was confirmed that there is no influence of a RB on KI-da/dN relation.

A fracture criterion of rubber-like materials under plane stress conditions

In this work, we attempt to derive a fracture criterion for filled and unfilled elastomer vulcanizates and thermoplastics from a set of experimental data. Firstly, fracture criteria reported in the literature have been applied to experimental data obtained from tests including various loading modes (simple tension, equal biaxial tension and biaxial tension) and performed on four materials: a natural rubber (NR), a styrene butadiene rubber (SBR), a polyurethane (PU) and a thermoplastic elastomer (TPE). Then, a new failure criterion based on an equivalent elongation concept is proposed. This equivalent elongation seems to be linearly dependent on a given biaxiality ratio n = ( ln ( λ 2 b ) / ln ( λ 1 b ) ) , which leads to expressing the principal elongations at break as functions of both the biaxiality n and two experimental parameters. Quite good agreement is highlighted when comparing the failure experimental data with the proposed criterion for the tested elastomers.

Creep Failure Behaviour of a 9CrMoNbV Weld Metal with Anisotropy Under a Biaxial Loading State

The ‘bulk’ material creep failure behaviour of an anisotropic 9CrMoNbV weld metal, under biaxial loading conditions, was investigated, using creep damage analyses with a ‘unit cell’ model. The model consists of a columnar region and a weaker ‘equiaxed’ (fine-grained and coarse-grained) region. Creep damage analyses were conducted using a single-variable Kachanov-type damage law, for which the material constants were obtained from experimental data. The bulk material creep rupture lives, under a range of biaxial load ratios, were determined, including the effects of a triaxial stress state parameter for the material. The typical failure modes are described and isochronous creep rupture curves and master load loci are presented.

Simulation of dynamic ductile crack growth using strain-rate and triaxiality-dependent cohesive elements

Rate-sensitive and triaxiality-dependent cohesive elements are used to simulate crack growth under quasi-static and dynamic loading conditions. The simulations are performed for a middle-cracked tension M(T) specimen made of an aluminum alloy (6XXX series). To consider the effect of stress triaxiality and strain rate on the cohesive properties, a single plane strain element obeying the constitutive equations of a rate-dependent Gurson type model has been used. The single element is loaded under various stress biaxiality ratios and strain rates and the obtained stress–displacement curves are considered as traction separation law for the cohesive elements. These curves are used for analyzing the aluminum M(T) specimen. The qualitative effects of constraint, strain rate, inertia and stress waves on the energy absorption of the specimen and crack growth are discussed.

Mechanism-based Failure Laws for Biaxially Compressed IM7/8551-7 Graphite–Epoxy Laminates

Failure mechanisms and stress–strain behaviors have been investi- gated for [15]6s,[30]12s, and [45]12s graphite–epoxy (IM7/8551-7) laminates under in-plane biaxial compression using a cruciform biaxial test frame and microscopic examination of the load-interrupted samples. The loading confinement ratio R is varied from 0 to nearly 1.0 to measure the sensitivity of sample failure mechanisms and stress–strain behaviors to different stress states. The failure modes for each orientation are found to be strongly confinement-ratio-dependent. For R 1/4 0, all the samples failed by in-plane shearing on a plane aligned with the fiber direction. As the confinement ratio is increased, the in-plane failure mode in [30]12s, and [45]12s samples transitioned to out-of-plane shearing at R 1/4 0.25 and 0.5, and multiple delamination at R 1/4 0.75 and 1.0. For the [15]6s samples, the failure modes transition to fiber buckling at R 1/4 0.25 and then out-of-plane shearing at R 1/4 0.5, 0.75, and 1.0. Microscopic examination of the load-interrupted samples confirms the source of the individual delaminations to be the wing cracks associated with the angled shear cracks in the out-of-plane direction. The classical laminate theory in combination with the standard rule of mixture is used to calculate the maximum shear stress in the matrix and the fibers. The failure data conform well with a Mohr–Coulomb-type shear failure law when applied to the fibers but not to the matrix. Thus, fiber shearing appears to be the failure-setting mechanism in this material under all material orientations and biaxiality ratios.

Fully plastic J-integral solutions for surface cracked plates under biaxial loading

In this paper, surface cracked plates under biaxial tension are studied. Three-dimensional elastic–plastic finite element analyses have been carried out to calculate the J-integral for surface cracked plate for a wide range of geometry, biaxiality and material properties. Fully plastic J-integral solutions along the front of the surface cracks are presented for Ramberg–Osgood power law hardening material of n = 3, 5, 10 and 15. Geometries considered are a/ c = 0.2, 1.0 and a/ t = 0.2, 0.4, 0.6 and 0.8 and the biaxial ratios of 0, 0.5 and 1. Based on these results, the J-integral along the crack front for general elastic–plastic loading conditions can be estimated using the EPRI scheme. These solutions are suitable for fracture analyses for surface cracked plates under biaxial loading.

Bridging Interactions in Ceramics and Consequences on Crack Path Stability

An important fracture mechanics parameter governing path stability of growing cracks is the biaxiality ratio, i.e. the ratio of the T-stress and stress intensity factor. It is well known in general fracture mechanics that crack growth under positive biaxiality ratios is path-unstable. Any unavoidable mode-II loading must result in an increasing deviation from the initial straight crack plane. This holds for the most fracture mechanics test specimens used in tests on ceramic materials, for instance, edge-notched bending bars, CT, and DCB specimens. The theoretically predicted crack path stability is in disagreement with experimental findings reported in the literature on R-curve measurements, where R-curves were measured for crack lengths yielding high positive biaxiality ratios. Two possible reasons for this astonishing discrepancy between theory and experiments will be discussed.

Joining of fiber‐reinforced polymer tubes for high‐pressure applications

AbstractFiber‐reinforced polymer composites offer superior performance particularly in harsh environments; hence, they are recognized as an attractive material, especially for the transportation of pressurized fluids. However, an extensive use of these composites has been hampered, in part due to unsatisfactory solutions for the joining of subcomponents, and insufficient knowledge on the associated damage behavior. A favorable connection design for a piping system can be an adhesively bonded joint. In this study, a unique adhesive injection technique is presented that joins composite pipe sections using filament‐wound overlap sleeve couplers. The purpose of the present study was to characterize the performance and associated damage behavior of a prototype‐size pipe structure joined by the above procedure. Internal pressure and axial traction were applied to specimens at various biaxial ratios. In addition to the experimental investigation, the joint geometry was also modeled numerically employing the finite element technique. This yielded a better understanding of the damage behavior and enabled a parametric study that provided recommendations for an improved joint design. POLYM. COMPOS., 27:99–109, 2006. © 2005 Society of Plastics Engineers

Multi-axial fatigue behaviour of a severely notched carbon steel

The paper deals with multi-axial fatigue strength of notched specimens made of C40 carbon steel (normalised state), subjected to combined tension and torsion loading, both in-phase and out-of-phase ( Φ=0 and 90°). V-notched specimens have been tested under two nominal load ratios, R=−1 and 0, while keeping constant and equal to the unity the biaxiality ratio, λ=σ a/ τ a. All specimens have the same geometry, with notch tip radius and depth equal to 0.5 and 4 mm, respectively, while the V-notch angle is equal to 90°. The results determined are discussed together with those deduced under pure tension or torsion loading on plain and notched specimens as well as on small shafts with shoulders. The application of an energy-based approach allows all the fatigue data obtained from the notched specimens to be summarised in a single scatter band, in terms of the total strain energy density evaluated at the notch tip against cycles to failure.

Engineering assessment of ductile tearing in uniaxial and biaxial tension

To decide between clearly different approaches for engineering assessment of plane stress tearing, we performed uniaxial and biaxial tensile tests on middle-cracked specimens at various in-plane constraint states. Attention was focused on determination of the crack tip opening spacing δ n, crack tip opening angle ψ c, crack mouth opening angle α s, energy dissipation rate R, and specific work of fracture A s. Our experimental results demonstrate that the values of δ n, ψ c, α s, R, and A s for a high-strength low-hardening aluminium alloy all depend on the specimen geometry, its size, and the load biaxiality ratio. However, assessment of ductile tearing by interconnected characteristic quantities α s and A s is more preferable over the use of δ n, ψ c, and R values for a number of basically important reasons discussed in this paper.

Effects of Biaxial Stress Condition for Fatigue Properties of Magnesium Alloy

Fatigue crack propagation tests of magnesium alloy were conducted under conditions of biaxial and uniaxial loading by using a cruciform specimen with the biaxial fatigue tester. The purpose of this study is to investigate the effect of biaxial stress on the fatigue crack growth properties ⊿KⅠ-da/dN. From these comprehensive experiments, the remarkable effect was found in the specific biaxiality ratio σx 0/σy 0 on the ⊿KⅠ-da/dN relationship. When biaxiality ratio was 0.5, it turned out that the fatigue crack propagation velocity of a magnesium alloy becomes very slow. In other biaxiality ratios, fatigue crack propagation velocity was influenced in some extent. Fatigue crack propagation velocity decreases a little as the stress which acts in parallel with a crack increases.

Experimental Study of Buckling Strength for Short Square Pipe Column of Carbon Steel Subjected to a Biaxial Bending Load (3rd Report, Upper Eccentric and Lower Coaxial Compressive Loding)

This paper is concerned with a biaxial bending compression experiment for the case of eccentric at the upper and axial at the lower ends on carbon steel square pipes in the short column range, supported with spherical seat. An empirical formula for calculating the eccentric bending compressive buckling stress σcre* of the carbon steel square pipes is presented as follows ; σcre*/σcr =1/ (1+ ao), where σcc, is equal to axial compressive buckling stress, ao is equal to factor of the eccentricity and biaxial ratio. The measurement reveals that the results calculated by this formula are in good agreement with those obtained experimentally for the short column range.

Stress intensity factors of a central slant crack with frictional surfaces in plates with biaxial loading

The stress intensity factor is a traditional topic in mechanics and there have been many solutions for many different cases. The closed frictional crack problem has been modeled in the rock mechanics field where fractures are mostly under compression. Further, the effect of finite plate dimensions under biaxial loading has not been considered in the literature. The key contribution of the present paper is to evaluate the effect of the crack length to plate width ratio on the mode I and II stress intensity factors (SIF) of a central slant crack with frictional surfaces in plates with biaxial loading of different patterns, i.e. tension-tension, tension-compression, compression-tension or compression-compression. A plane strain elastic two-dimensional finite element analysis was adopted. Crack length to plate width ratios equal to 0.1, 0.3 and 0.5 with biaxial ratios from −1 to 1, crack angles from 0° to 90° and friction coefficients from 0 to 1 were considered. Contact regimes and the effect of the crack length to plate width ratio were found dependent on biaxial ratio and pattern, friction coefficient and crack angle.

Yield surfaces for perforated plates with square arrays of holes

A symmetric model of a perforated plate containing a 3×3 array of circular holes, arranged in a square pattern, was chosen and elastoplastic finite element analyses were carried out to determine the limit stresses for both pitch and diagonal directions of loading, for different values of biaxiality ratios. Plane stress conditions were assumed and the Tresca and von Mises yield criteria were employed to obtain two different sets of results. Yield surfaces were constructed and ‘general cut-out factors’ were determined for four different ligament efficiencies. The FEM results obtained by the authors using the Tresca and von Mises yield criteria were compared with the corresponding results of [J. Pressure Vessel Technol. Trans. ASME (1975) 146–154] and [J. Pressure Vessel Technol. Trans. ASME (1997) 122–126], respectively. The results based on the Tresca yield criterion obtained by the present authors and those in [J. Pressure Vessel Technol. Trans. ASME (1975) 146–154] were found to agree well with each other. In the case of the von Mises yield criterion, the agreement with [J. Pressure Vessel Technol. Trans. ASME 122–126] is generally good. The estimates based on the Tresca yield criterion are seen to result in lower values of limit stresses and cut-out factors as compared to those based on the von Mises yield criterion. The difference is attributed to the yield criterion and the flow rule chosen for the analysis. The shape as well as the size of the yield surface was found to depend on the ligament efficiency.

T-stress solution for DCDC specimens

A finite element study is performed in order to determine the T-stress term for DCDC specimens with holes set off from the specimen centre line. In addition, mixed-mode stress intensity factors K I and K II are given and the biaxiality ratio β is computed from T and K I. The T-stress results are fitted and presented in a simple relation.

동력학 시뮬레이션에 의한 다축 랜덤하중 하에서 자동차 서브프레임의 고 되풀이수 피로손상 평가

A FEM-based analytical approach was used to evaluate the multiaxial high cycle fatigue damage of an automotive sub-frame. Elastic Multi Body Simulation (MBS) has been applied in order to determine the multiaxial load histories. The stresses due to these loads have been given by FE computation. These results have been used as the input for the multiaxial fatigue analysis. For the assessment of multiaxial high cycle fatigue damage, the signed von Mises, the signed Tresca, the absolute maximum principal stress and critical<br/> plane methods have been employed. In addition, the biaxiality ratio, a_e, the absolute maximum principal stress,<br/> σ₁ and the angle, ω_p' between σ₁ and the local x-axis, have been calculated to evaluate the stress state at each node.

Peak stress multipliers for thin perforated plates with square arrays of circular holes

A quarter symmetric part of a perforated plate containing a 3×3 square array of circular holes was analysed by the finite element method (FEM) to obtain the peak stress multipliers (PSMs) under membrane and bending loads for different biaxiality ratios. The PSMs for the membrane part were compared with Bailey and Hicks [J. Mech. Engng. Sci. 2 (1960) 2] and Hulbert and Neidenfuhr [J. Engng. Ind. Trans. ASME 37 (1965) 3] and show good agreement with the latter. The PSMs for the bending part were compared with those of Meijers' finite element results [J. Pressure Vessel Technol. Trans. ASME 108 (1986) 423] and show a maximum variation of about 10%. Photoelastic experiments were carried out to verify the FEM results. The distributions of stress around the periphery of the hole as well as along the ligaments have also been obtained. Correlations have been established for PSMs under various conditions.

Post-buckling analysis of elastic honeycombs subject to in-plane biaxial compression

Abstract In this paper, employing the homogenization theory and the microscopic bifurcation condition established by the authors, we discuss which microscopic buckling mode grows in elastic honeycombs subject to in-plane biaxial compression. First, we focus on equi-biaxial compression, under which uniaxial, biaxial and flower-like modes may develop as a result of triple bifurcation. By forcing each of the three modes to develop, and by comparing the internal energies, we show that the flower-like mode grows steadily if macroscopic strain is controlled, while either the uniaxial or biaxial mode develops if macroscopic stress is controlled. Second, by analyzing several cases other than equi-biaxial compression, it is shown that a second bifurcation from either the uniaxial or biaxial mode to the flower-like mode, which is distorted, occurs under biaxial compression in a certain range of biaxial ratio under macroscopic strain control. Finally, the possibility of macroscopic instability under biaxial compression is discussed.