The macroscopic yielding behaviour of polymers in multiaxial stress fields

Experimental data on yielding of polyoxymethylene (POM) and polypropylene (PP) have been obtained in a wide range of complex triaxial stress conditions. These complex triaxial stress states have been produced by superimposition of simple stresses such as uniaxial compression, uniaxial tension and pure shear on hydrostatic pressure of various intensities. The actual yield surfaces of both polymers were constructed using the data. The yield surface of POM is a cone-shaped with a pointed apex and straight edges, while the yield surface of PP is cone-lime and non-linear, also with a pointed apex. A yield criterion is shown to very closely predict the observed behaviour of both polymers.     

Viscoplasticity characteristics of heat-resisting steels in a multiaxial stress state

Results are presented of the experimental examination of the viscoplastic properties of 15Kh2MFA, 15Kh2NMFA, and VK2 (KP-100) heat-resisting steels simulating radiation-embrittled 15Kh2NMFA steel, at different ratios of the main stresses in the temperature range 20–350°C, carried out using a specially prepared method. The experimental results are used to draw conclusions according to which the generalized quasistatic (equilibrium) deformation diagram, obtained at a strain rate tending to zero, is invariant to the type of stress state, and also that the toughness factors of the examined steels are invariant to the type of stress, state and cumulated plastic strain in the entire temperature range examined.Translated from Problemy Prochnosti, No. 11, pp. 52–57, November, 1991.     

Interaction between crack-like defects in three-dimensional bodies

The authors describe the procedure and results of investigations by the photoelasticity method of the effect of interaction of defects on the stress intensity factor. The resultant data, essential for determining the permissible distances between the defects, can be used in rejecting components of equipment on the basis of the results of ultrasonic inspection.Translated from Problemy Prochnosti, No. 7, pp. 34–37, July, 1990.     

Damage zone development in PVC under a multiaxial tensile stress state

The irreversible deformation mechanisms of poly(vinyl chloride) with a semicircular notch under slow tensile loading have been studied as a function of sheet thickness. Initially, core yielding was observed in the optical microscope as two families of slip lines growing from the notch surface in the centre of the specimen. The size and shape of the core yielding zone could be described by plasticity analysis. A stress-whitened zone subsequently initiated near the tip of the slip line zone. The stress whitening was caused by 1 m voids that were visible in the scanning electron microscope. The mean stress for stress whitening was calculated to be 43.0±1.5 MPa by a plastic stress analysis of a pressure-dependent yield material. By assuming a constant mean stress along the boundary of the stress-whitened zone, the one-dimensional shift of the elastic stress distribution was obtained. At higher stresses, hinge shear and intersecting shear were observed for thick and thin sheet, respectively.     

Cavity growth from crack-like defects in soft materials

We study the growth and failure of small crack-like defects in elastomers under hydrostatic tension. Since the elastic modulus of elastomers are typically very small in comparison with the cohesive strength, crack-like defects can grow into spherical-like cavities before failure. The condition of crack growth or cavity failure is determined using Griffith's fracture criterion, that is, failure of the cavity or crack growth occurs when the energy release rate of the crack-like defect exceeds the surface energy. Three different material behaviors are considered. In the first, we use a power law material model where the strain energy density function w is \displaystylew=\frac2n([1+(I ₁–3)]ⁿ–1), where I ₁ is the sum of squares of the principal stretches, is the infinitesimal shear modulus, and n0 are material constants. In the second case, we consider a Mooney-Rivlin material, which describes the deformation of pressure sensitive adhesives. In the final case, we consider a material model proposed by Gent (1996), which takes into account the condition that a molecular network will fail at some critical stretch ratio. The dependence of the energy release rate on the applied hydrostatic tension is determined using a large strain finite element method. Comparisons are made between our analysis and a previous result of Gent and Wang (GW) (1991), as well as a result of Williams and Schapery or WS (1965). The role of strain hardening in determining the critical applied hydrostatic tension to fail a cavity is examined by comparing the numerical results using the above three constitutive models.     

Life estimation for high-strength materials under cyclic loading in the multiaxial stress state

The life of high-strength materials under cyclic loading in the multiaxial stress state is experimentally estimated using the deformation-kinetic criterion. Translated from Problemy Prochnosti, No. 2, pp. 139–143, March–April, 2009.     

Evaluation of viscoplastic properties of VNS-25 high-strength steel in a multiaxial stress state

Investigation results for VNS-25 high-strength steel in a multiaxial stress state under stepwise cyclic loading were presented. The applicability of the viscoelastoplastic model to studying structural materials was substantiated experimentally. __________ Translated from Problemy Prochnosti, No. 6, pp. 122–127, November–December, 2007.     

Study on creep mechanical behaviour of P92 steel under multiaxial stress state

The creep mechanical behaviour of P92 steel at 650°C has been studied by experimental research and finite element analysis. During the creep of P92 steel, there existed the notched strengthening effect, which was influenced by the shapes of the notch and the nominal stress. Under the condition of the same notch depth, the creep life enhancement factor increased with decreasing notched radius or the increase of stress. The multiaxial stress caused by the notch effect had a significant influence on the evolution of the microstructure and resulted in a transforming tendency from ductile to brittle at the root of the notch. The fracture position varied with the shapes of the notch: the U shaped notch started to fracture at the root of the notch, while the C shaped notch in the centre of the specimen. The creep process of notched specimens was simulated by embedding Kachanov–Rabotnov creep damage constitutive model into the interface program of finite element software. The result showed that damage distribution of notched specimens varied during the process of creep. The maximum damage location at the end of creep depended on the notch shape: with larger notch radius the maximum damage location was in the centre, while smaller radius of notch specimens was near the notch root, which was consistent with the analysis of the fracture morphology.     

The propagation of cracks and crack-like defects in thin adhered polymer films

The strain energy release rateG of a through-thickness crack in a thin film that adheres to a rigid substrate is shown to vary linearly with the film thickness at constant film stress.G is normally small, so adhered polymer films are only expected to crack in the presence of an aggressive environmental agent unless the polymer is very brittle. A minimum film thickness for cracking is likely to be observed. The propagation of crack-like defects in a polyimide in the presence of xylene was examined experimentally. The defects grew at a constant rate (independent of their length) that increased rapidly with film thickness. The minimum film thickness for defect growth was found to be about 2m.     

Three energy-based multiaxial HCF criteria for fatigue life determination in components under random non-proportional stress fields

The prominent high cycle fatigue (HCF) criteria have been generally proposed based on definition of an equivalent stress that is mainly a modified version of a static failure criterion or a static yield function. One or more effects including the mean normal and shear stresses, different phase shifts or random frequencies of the stress components, relative instantaneous time variations of the stress components, relative time locations of the extrema of the time histories of the stress components, etc. have not been considered by many of the previously proposed criteria. In the present paper, based on the proposed instantaneous stress amplitude and mean stress concepts, three new energy-based HCF criteria are proposed to overcome the mentioned shortcomings. A relevant fatigue life assessment algorithm is proposed and results of the prominent criteria are compared with results of the proposed criteria as well as the experimental results prepared by the author. To introduce a comprehensive study, the criteria are examined for components with complicated geometries under proportional, non-proportional and random loadings. Results confirm the efficiency and accuracy of the proposed criteria. Furthermore, it is deduced that the Liu–Zenner type criteria which include the hydrostatic stress implicitly are more accurate than the Papadopoulos-type criteria that consider the hydrostatic stress explicitly.     

Evaluation of the endurance of heat-resisting steels in soft pulsed loading in a multiaxial stress state

Institute of Strength Problems, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Problemy Prochnosti, No. 5, pp. 36–39, May, 1989.     

Studies on damage accumulation kinetics in a metal under cyclic loading in the multiaxial stress state

Results of experimental investigations of deformation behavior for 10GN2MFA steel under cyclic loading in the multiaxial stress state are presented. The effect of a stress state on homogeneity factor variations that represents a measure of metal damage is shown.     

Three-dimensional stress and deformation fields around flat and slant cracks under remote Mode I loading conditions

This paper investigates the phenomenon of slant fracture observed in stable tearing tests of many ductile materials, where an initially flat crack, loaded under remote Mode I conditions, tends to grow into a slant crack and stay in the slant configuration until final fracture. In an effort to identify potential reasons why cracks prefer to grow in a slant manner, three-dimensional finite element analyses of crack-front stress and deformation fields in Arcan-type specimens containing a flat or slant crack are performed under elastic–plastic and remote Mode-I loading conditions. In particular, the crack-tip opening displacement (COD) at a position behind the crack tip, the mean stress, the effective stress, and a constraint factor (defined as the ratio of the mean stress and effective stress) are studied and compared for the two types of cracks. Analysis results reveal several stress/deformation field variations around flat and slant cracks under identical remote loading conditions. First, close to the crack front, the COD of a slant crack is greater than that of a flat crack. Second, at the specimen’s mid-plane, a flat crack leads to a higher constraint value ahead of the crack than a slant crack. Third, the effective stress ahead of a slant crack is greater than that ahead of a flat crack, especially close to the crack front. The above results seem to suggest that slant fracture may be preferred because a slant crack enhances the driving force in the form of a higher near-tip COD value and because a shearing type of failure is promoted in the case of a slant crack compared to a tensile type of failure in the case of a flat crack.