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1.
Based on detailed three-dimensional (3D) finite element analyses, elastic fields in front of blunt V-notches in finite thickness plates subjected to uniaxial far-end tensile stress have been investigated. By comparison with the corresponding planar V-notch fields and 3D through-thickness sharp crack fields, various aspects of the 3D fields of the blunt V-notches in finite thickness plates are revealed: (1) The plate thickness and notch angle have obvious effects on the stress concentration factor (SCF) K t, which is higher in finite thickness plates than in the plane stress and plane strain cases. When the notch angle is smaller than 90°, the SCF is insensitive to the notch angle, but has close relation with the dimensionless plate thickness. With the notch angle increasing further, the SCF decreases and the effect of dimensionless plate thickness on it becomes weaker. (2) For any notch angle considered, the variation of the opening stress yy normalized by its value yy0 at the notch-root with the distance x from the root normalized by the root-radius , is insensitive to the plate thickness and coincides well with the two-dimensional (2D) planar solution. (3) The 3D distribution of the out-of-plane constraint factor T z=zz/(yy+xx) is controlled by the plate thickness (B), the notch-radius () as well as the notch angle (), but for deeper V-notches with 90°, the distribution of T z coincides well with that of a U-notch as well as a sharp 3D through-thickness crack and an explicit empirical expression of T z is presented. (4) The distribution of the in-plane stress ratio T x=yy/xx in front of the 3D V-notch is nearly independent of the plate thickness and coincides well with the corresponding 2D solutions when the opening angle is smaller than 120°. (5) The gradient of the out-of-plane strain zz is significant near the free surface in finite thickness plates. On the free surface, the zz can be 3.5 times the value on the mid-plane, and the through-thickness gradient of the zz increases with decreasing notch angle. It is of interest to note that most of the field quantities ahead of V-notches are insensitive to the notch angles when the notch angle is smaller than 90°.  相似文献   

2.
In fatigue crack growth analysis it is essential to know the stress distributions in the neighbourhood of stress raisers. If such distributions ahead of the uncracked notch are known, stress intensity factors may be obtained via the weight function or other methods. The procedure described in the present paper reconsiders the principal elastic stress expressions already reported by the authors for infinite plates with semi-infinite symmetric V-shaped notches and adapts them to some practical cases, in which the mutual influence of the notches as well as that of the plate finite size play an important role in stress distributions. The aim is therefore to give an approximate close-form solution for the longitudinal stress, valid for the entire ligament length, namely from notch tip to notch tip. Theoretical and numerical stress values are compared on this line, examining plates with semicircular, V and U-shaped notches subjected to remote uniaxial tension. This revised version was published online in August 2006 with corrections to the Cover Date.  相似文献   

3.
By making use of the generalized plane strain hypothesis, an approximate stress field theory has been developed according to which the three‐dimensional governing equations lead to a system where a bi‐harmonic equation and a harmonic equation should be simultaneously satisfied. The former provides the solution of the corresponding plane notch problem, and the latter provides the solution of the corresponding out‐of‐plane shear notch problem. The system can be applied not only to pointed three‐dimensional V‐notches but also to sharply radiused V‐notches characterized by a notch tip radius small enough. Limits and degree of accuracy of the analytical frame are discussed comparing theoretical results and numerical data from FE models.  相似文献   

4.
The elastic stress distributions in some edge-notched geometries have been estimated from Creager and Paris's and Neuber's expressions. Close to the notch root, these approximate solutions agree well with the finite element results. Further away from the notch, the approximate methods give overestimations. A simple formula derived from Creager and Paris's expression provided accurate stress concentration factor solutions for some edge-notched geometries.  相似文献   

5.
A fatigue strength parameter for (seam-)welded joints is presented which is based on the averaged elastic strain energy density (SED) criterion applied to full circle and semicircular ‘control volumes’, the latter centred by the expected crack path. The parameter is applicable both at weld toes and weld roots, at least in the medium-cycle and high-cycle fatigue range where elastic conditions are prevailing. Based on a rectangular slit-plate model representing the weld root and analysed by the finite element method, the effect of the following influencing conditions is investigated: tension loading (mode 1) and shear loading (mode 2), slit-parallel tension loading acting on a rounded slit tip, pointed slit tip versus small-size key-hole at the slit tip, semicircle and narrow sector versus full circle or full sector SED evaluations, distortional SED versus total SED under plane strain conditions. The following conclusions are drawn from the numerical results. The SED approach should be based on the full circle or full sector evaluation of the total SED, with R0 = 0.28 mm for steels. In cases of a markedly unilateral angular SED distribution, the semicircle evaluation centred by the expected crack path is more appropriate. The use of small-size reference notches instead of pointed notches provides no advantage. The endurable remote stresses for fatigue-loaded welded joints according to the SED approach are well in correspondence with those according to the fictitious notch rounding approach. High accuracy of the results can already be achieved with a rough meshing at the pointed notches.  相似文献   

6.
Three-dimensional finite element analyses were performed on plates with a through-the-thickness crack. Global-local finite element technique with sub-modeling was used to achieve the refinement required to obtain an accurate stress field. The existence of a weaker singularity was verified, and a model was proposed to explain the behavior of stresses in the boundary layer. This model is able to account for the competing interaction between the inverse square root singular term and the vertex singular term. The energy release rate was calculated using the modified crack closure method and energy balance. A simple technique without 3-D calculation was suggested for evaluating an approximate 3-D stress intensity factor at the mid-plane. The effect of plate thickness on the size of the three-dimensional region was studied, and the validity of two-dimensional linear elastic fracture mechanics was discussed.  相似文献   

7.
In this study, generalized stress intensity factors KI,λ1, KII,λ2, and KIII,λ4 are calculated for a V-shaped notched round bar under tension, bending, and torsion using the singular integral equation of the body force method. The body force method is used to formulate the problem as a system of singular integral equations, where the unknown functions are the densities of body forces distributed in an infinite body. In order to analyze the problem accurately, the unknown functions are expressed as piecewise smooth functions using three types of fundamental densities and power series, where the fundamental densities are chosen to represent the symmetric stress singularity and the skew-symmetric stress singularity. Generalized stress intensity factors at the notch tip are systematically calculated for various shapes of V-shaped notches. Normalized stress intensity factors are given by using limiting solutions; they are almost determined by notch depth alone, and almost independent of other geometrical parameters. The accuracy of Benthem-Koiter’s formula proposed for a circumferential crack is also examined through the comparison with the present analysis.  相似文献   

8.
In the recent literature some researchers proposed the use of the mean value of the Strain Energy Density (SED) over a well-defined control volume for static and fatigue strength assessment of components weakened by sharp V-shaped notches. In those papers the SED was expressed in terms of Notch Stress Intensity Factors (NSIFs), whose accurate evaluation needs a very fine mesh when based on local stress determined along the notch bisector. This contribution shows that when the material behaviour is ideally linear elastic or obeys a power hardening law, the mean value of the SED over the control volume can also be precisely determined from a coarse mesh. This result is of interest in the practical application of the SED approach to real components. Eventually, NSIFs can be evaluated a posteriori, just on the basis of the local SED. While discussing some results from elastic-plastic analyses carried out on a V-notched plate under tension loading and on a V-notched round bar under torsion, the different roles played by local and large scale yielding are highlighted. The result is used here to provide a justification for the different slopes, 3.0 and 5.0, reported by Eurocode 3 and other Standards in force for welded details subjected to tensile or shear stresses, respectively.  相似文献   

9.
Detailed full-field three-dimensional (3D) finite element analyses have been conducted to study the out-of-plane stress constraint factor Tz around a quarter-elliptical corner crack embedded in an isotropic elastic plate subjected to uniform tension loading. The distributions of Tz are studied in the forward section (0° ? θ ? 90°) of the corner cracks with aspect ratios a/c of 0.2, 0.4, 0.5, 0.6, 0.8 and 1.0. In the normal plane of the crack front line, Tz drops radially from Poisson’s ratio at the crack tip to zero beyond certain radial distances. Strong 3D zones (Tz > 0) exist within a radial distance r/a of about 4.6-0.7 for a/c = 0.2-1.0 along the crack front, despite the stress-free boundary conditions far away. At the same radial distance along the crack front in the 3D zones, Tz increases from zero on one free surface to a peak value in the interior, and then decreases to zero on another free surface. The distributions of Tz near the corner points are also discussed. Empirical formulae describing the 3D distributions of Tz are obtained by fitting the numerical results, which prevail with a sufficient accuracy in the valid range of 0.2 ? a/c ? 1.0 and 0° ? θ ? 90° except very near the free surfaces where Tz is extremely low. Combined with the K-T solution, the transition of approximate plane-stress state near the surfaces to plane-strain state in the interior can be characterized more accurately.  相似文献   

10.
Weld bead geometry cannot, by its nature, be precisely defined. Parameters such as bead shape and toe radius vary from joint to joint even in well-controlled manufacturing operations. In the present paper the weld toe region is modelled as a sharp, zero radius, V-shaped notch and the intensity of asymptotic stress distributions obeying Williams’ solution are quantified by means of the Notch Stress Intensity Factors (NSIFs). When the constancy of the angle included between weld flanks and main plates is assured and the angle is large enough to make mode II contribution non-singular, mode I NSIF can be directly used to summarise the fatigue strength of welded joints having very different geometry. By using a large amount of experimental data taken from the literature and related to a V-notch angle of 135°, two NSIF-based bands are reported for steel and aluminium welded joints under a nominal load ratio about equal to zero. A third band is reported for steel welded joints with failures originated from the weld roots, where the lack of penetration zone is treated as a crack-like notch and units for NSIFs are the same as conventional SIF used in LEFM. Afterwards, in order to overcome the problem related to the variability of the V-notch opening angle, the synthesis is made by simply using a scalar quantity, i.e. the mean value of the strain energy averaged in the structural volume surrounding the notch tips. This energy is given in closed form on the basis of the relevant NSIFs for modes I and II and the radius RC of the averaging zone is carefully identified with reference to conventional arc welding processes. RC for welded joints made of steel and aluminium considered here is 0.28 mm and 0.12 mm, respectively. Different values of RC might characterise welded joints obtained from high-power processes, in particular from automated laser beam welding. The local-energy based criterion is applied to steel welded joints under prevailing mode I (with failures both at the weld root and toe) and to aluminium welded joints under mode I and mixed load modes (with mode II contribution prevailing on that ascribable to mode I). Surprising, the mean value of ΔW related to the two groups of welded materials was found practically coincident at 2 million cycles. More than 750 fatigue data have been considered in the analyses reported herein.  相似文献   

11.
The authors develop an eigth-order model for bending of transversally isotropic plates and use integral transforms and a collocation method to form a line-spring model for a cracked plate. The eigth-order model allows satisfaction of the three standard plate bending boundary conditions; the normal moment, twisting moment, and transverse shear force, and an additional shear stress resultant that allows analysis of transverse normal stresses near the crack tip. The line-spring model is used to develop geometry correction factors for bending of finite-thickness plates, accounting for transverse shear deformation and pressurization of the plate near the crack tip. The line-spring model is then applied to the problem of a plate with a reinforced crack, and the results are used to validate an interpolation solution based on an energy method. While not explicitly analysed, the models are applicable to many problems, including bending of bonded repairs, fracture and fatigue of composite and layered materials, surface cracks, crack tip plasticity and crack closure or crack face interaction.  相似文献   

12.
A geometrically nonlinear, two-dimensional (2D) finite element analysis has been performed to determine the stress and strain distributions across the adhesive bond thickness of composite single-lap joints. The results of simulations for 0.13 and 0.26 mm bond thickness are presented. Using 2-element and 6-element mesh schemes to analyze the thinner bond layer, good agreement is found with the experimental results of Tsai and Morton. Further mesh refinement using a 10-element analysis for the thicker bond has shown that both the tensile peel and shear stresses at the bond free edges change significantly across the adhesive thickness. Both stresses became increasingly higher with distance from the centerline and peak near but not along the adherend–adhesive interface. Moreover, the maximum shear and peel stresses occur near the overlap joint corner ends, suggesting that cohesive crack initiation is most likely to occur at the corners. The dependence of stress and corresponding strain distributions on bond thickness and adhesive elastic modulus are also presented. It is observed that the peak shear and peel stresses increase with the bond thickness and elastic modulus.  相似文献   

13.
利用DSC对预应变TiNi形状记忆合金丝在恒应力约束下的马氏体不完全逆相变进行了研究,发现不完全相变热循环样品在第二次自由态加热过程中出现两步马氏体逆转变和两段应变回复现象.分析认为:经过恒应力约束下的不完全逆相变后,TiNi样品中存在不同的马氏体,在随后的加热过程中先后逆转变,产生两段回复应变.  相似文献   

14.
This paper studies interfacial mechanical behavior of laminate beams, consisting of two piezoelectric facial sheets and an elastic core. The study is based on coupled multi-filed finite element formulation. The emphasis is placed on mechanical and electric behavior of interfaces between piezoelectric material and elastic material, including effect of geometrical parameters, stress distribution and stress concentration near free edge of the beam subjected to coupling electric and mechanical loads. In particular, various parametric effect of laminate beam is explored and some conclusions are presented which may be useful for designing laminate beam and minimizing stress concentration at the free edges of the beam.  相似文献   

15.
A large bulk of static test results carried out on notched specimens are presented in a unified way by using the mean value of the strain energy density (SED) over a given finite-size volume surrounding the highly stressed regions. In plane problems, when cracks or pointed V-notches are considered, the volume becomes a circle or a circular sector, respectively, with R C being the radius. R C depends on the fracture toughness of the material, the ultimate tensile strength and the Poisson's ratio. When the notch is blunt, the control area assumes a crescent shape and R C is its width as measured along the notch bisector.
About 900 experimental data, taken from recent literature, are involved in the local SED-based synthesis. They have been obtained from (a) U- and V-notched specimens made of different materials tested under mode I loading; (b) U- and V-notched specimens made of polymethyl-metacrylate (PMMA) and an acrylic resin, respectively, tested in mixed, I + II, mode; (c) U-notched specimens made of ceramics materials tested under mode I.
The local SED values are normalized to the critical SED values (as determined from unnotched specimens) and plotted as a function of the R / R C ratio. A scatter band is obtained whose mean value does not depend on R / R C, whereas the ratio between the upper and the lower limits are found to be about equal to 1.6. The strong variability of the non-dimensional radius R / R C (ranging here from about zero to around 1000) makes stringent the check of the approach based on the mean value of the local SED on a material-dependent control volume.  相似文献   

16.
To explore constraint effects on fully plastic crakc-tip fields, analytical solutions are examined for mode-I, II and III loading in non-hardening materials under plane strain conditions. The results reveal that under mode-II and III loading the crack-tip stress fields are unique, and thus can be characterized by a `single parameter'. Under mode-I loading, however, the crack-tip stress field is non-unique but can be characterized by two sets of solutions or `two parameters'. One set of the solutions is the well-known Prandtl field and the other is a plastic T-stress field. This conclusion corroborates the observation of McClintock (1971) that the slip-line field is non-unique for plane strain tensile cracks. A two-term plastic solution which combines the Prandtl field and the plastic T-stress field with two parameters B 1 and B 2 can then characterize the crack-tip stress field of plane strain mode-I crack over the plastic region and quantify the magnitude of crack-tip constraints. These characters are similar to those for hardening materials. Analyses and examples show that the two-term plastic solution can match well with the slip-line field or finite element results over plastic region. Thus the parameters B 1 and B 2 can be used to characterize the constraint level for mode-I finite-sized crack specimens in non-hardening materials under plane strain conditions.  相似文献   

17.
The definition of a measure of strain, referred to as the bi-configuration strain tensor, centres on the difference between the left Cauchy-Green deformation tensor and its inverse. A new measure of stress, coined the bi-configuration stress tensor, has been defined. This measure of stress refers the traction in the current configuration jointly to the referential and spatial configurations, that is, to an effective element of area identified as an element of bi-configuration area. The stress and strain tensors are assumed to be constitutively related by a finite strain form of a generalised Hooke's law. The predictions obtained from the proposed constitutive equation are compared with the observed mechanical behaviour of various test materials. Comparison with experiment centres on biaxial stress measurements in various simple modes of deformation identified by way of a generalised stress-strain relation. The predictions from the proposed constitutive theory are in good accord with the results of experiment.  相似文献   

18.
19.
为了深入研究刀具几何参数对KDP晶体超精密切削过程的影响,以及等效应力和应变产生的原因及变化规律,采用商用有限元软件(Marc)对KDP晶体的超精密切削过程进行了有限元仿真,建立了KDP晶体超精密切削加工中应力和应变预测模型.仿真结果表明,KDP晶体超精密加工过程中等效应力主要集中在第一和第二变形区,等效应变主要集中在第二和第三变形区.研究表明,本文所建立的等效应力和应变预测模型是有效的,有限元仿真值与预测值之间的误差可以控制在10%以内.  相似文献   

20.
A two-step method based on modal strain energy is presented for damage identification in thin plates. In the first step, damage is localized with the modal strain energy change ratio approach. A method is proposed to weaken the ‘Vicinity Effect’, thus reduces the false alarms in the localization of damage. In the second step, the damage extents of the suspected damaged elements are obtained iteratively with modal strain energy change sensitivity-based finite element model updating approach. Model reduction is introduced to eliminate the measurement of rotation degrees-of-freedom in the mode shapes. Two numerical examples are studied to demonstrate the effectiveness and robustness of the proposed method. Both single damage and multiple damage cases are studied and good identification results are obtained. The effect of measurement noise on the identification results is investigated.  相似文献   

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