The Effects of Nonproportional Loading on the Elastic-Plastic Crack-Tip Fields

2016 ◽  
Vol 853 ◽  
pp. 83-87 ◽  
Author(s):  
Zhao Yu Jin ◽  
Xin Wang ◽  
Dun Ji Yu ◽  
Xu Chen

In this paper, the loading path effects on the plane strain elastic-plastic crack-tip stress field are investigated computationally. Three different loading sequences include one proportional loading and two non-proportional loading paths are applied to the modified boundary layer (MBL) model under small-scale yielding conditions. For the same external displacement field applied at the outer boundary of the MBL model, the mode I K field and T-stress field combined as the different loading paths are applied to investigate the influence of the nonproportional loading. The results show that for either the compressive or tensional T-stress, the loading path which applied K field followed by T field generates the lower crack-tip constraint. There is only slightly difference between the proportional loading path and that with the T-stress field following by K field. The results show that it is very important to include the load sequence effects in fracture analysis when dealing with nonproportional loading conditions.

Author(s):  
Zhaoyu Jin ◽  
Xin Wang

In this paper, the loading path effect on the elastic-plastic crack-front stress field in a thin plate is investigated. There different loading sequences include one proportional loading and two non-proportional loading paths are applied to the 3-D modified boundary layer (MBL) model under small-scale yielding conditions. For the same external displacement field applied at the outer boundary of the 3-D MBL model, the mode I K field and T-stress field combined as the different loading path is applied to investigate the influence of the nonproportional loading. The results show that for either the compressive or tensional T-stress, the loading path which applied K field followed by T field generates the lower crack-tip constraint. There is only slightly difference between the proportional loading path and the T-stress field following by K field loading path. The results show that it is very important to include the load sequence effects in fracture analysis when dealing with nonproportional loading conditions.


Author(s):  
David W. Beardsmore ◽  
J. K. Sharples ◽  
C. J. Madew ◽  
M. Jackson

It is well known that the crack tip stress and strain fields for a crack in an elastic-plastic body depend on the crack tip contour integral J, the Q-stress, and the elastic-plastic properties of the material. This dependence is the fundamental basis of conventional two-parameter J-Q fracture mechanics assessments. It is normally assumed that the crack is created in an unstressed body, or else is inserted concurrently into an existing non-zero stress and strain field such that the crack tip fields build up monotonically and dominate at the crack tip. In such cases, the crack may be regarded as stationary and the J-Q procedure is valid provided that care is taken to calculate J and Q properly when initial stress and/or strains exist. When a crack is introduced progressively and quasi-statically into a component, the location of the crack tip will move along a distinct path. If the component contains residual stress and this is of a significant size along the crack tip path, a re-distribution of the residual stress will occur as the crack tip moves. Specifically, the stress field ahead of the crack tip will unload as the crack tip advances so that non-proportional loading will occur behind the advancing crack tip. In elastic-plastic materials, a wake of plasticity will usually be deposited in the material behind the moving or growing crack tip. Similar effects will also occur when a stationary crack extends due to critical or sub-critical processes. The presence of a plastic wake alters the stress and strain fields at the crack tip so that they do not generally match the fields of a stationary crack. Moreover, J and Q may not describe the stress and strain fields, invalidating the use of the fracture mechanics procedure for such cases. In this paper, a Finite Element analysis of J and Q is carried out for a quasi-statically extending crack inserted in a strip of elastic-plastic material containing an initial residual stress field. Care is taken to model the crack tip conditions appropriately as the crack extends and J is determined using the JEDI post-processing program which can allow for the effects of initial plastic strains and non-proportional loading. An assessment is made of the crack tip field and the likelihood of further extension or fracture is made using local approach models. The analysis considers both cleavage and ductile fracture. The extent of the relationship between J and Q and the crack tip fields is established and the validity of the J-Q procedure to such cases is discussed. The paper considers whether the procedure is conservative when J and Q are determined from an analysis of a stationary crack of the same size inserted into the same initial field.


2007 ◽  
Vol 567-568 ◽  
pp. 141-144 ◽  
Author(s):  
Pierre Evrard ◽  
Veronique Aubin ◽  
Suzanne Degallaix ◽  
Djimedo Kondo

In order to model the elasto-viscoplastic behaviour of an austenitic-ferritic stainless steel, the model initially developed by Cailletaud-Pilvin [1] [2] and used for modeling single-phase polycrystalline steel is extended in order to take into account the bi-phased character of a duplex steel. Two concentration laws and two local constitutive laws, based on the crystallographic slips and the dislocation densities, are thus simultaneously considered. The model parameters are identified by an inverse method. Simple tests among which tension test at constant strain rate and at different strain rates and uniaxial tension-compression test are used during the identification step. The predictive capabilities of the polycrystalline model are tested for non-proportional loading paths. It is shown that the model reproduces the over-hardening experimentally observed for this kind of loading paths. Then, yield surfaces are simulated during a uniaxial tension-compression test: it is shown that the distortion (i.e. plastic anisotropy induced by loading path) is correctly described.


2020 ◽  
Author(s):  
Carolina Giorgetti ◽  
Marie Violay

<p>Despite natural faults are variably oriented to the Earth's surface and to the local stress field, the mechanics of fault reactivation and slip under variable loading paths (sensu Sibson, 1993) is still poorly understood. Nonetheless, different loading paths commonly occur in natural faults, from load-strengthening when the increase in shear stress is coupled with an increase in normal stress (e.g., reverse faults in absence of the fluid pressure increase) to load-weakening when the increase in shear stress is coupled with a decrease in normal stress (e.g., normal faults). According to the Mohr-Coulomb theory, the reactivation of pre-existing faults is only influenced by the fault orientation to the stress field, the fault friction, and the principal stresses magnitude. Therefore, the stress path the fault experienced is often neglected when evaluating the potential for reactivation. Yet, in natural faults characterized by thick, incohesive fault zone and highly fractured damage zone, the loading path could not be ruled out. Here we propose a laboratory approach aimed at reproducing the typical tectonic loading paths for reverse and normal faults. We performed triaxial saw-cut experiments, simulating the reactivation of well-oriented (i.e., 30° to the maximum principal stress) and misoriented (i.e., 50° to the maximum principal stress), normal and reverse gouge-bearing faults under dry and water-saturated conditions. We find that load-strengthening versus load-weakening path results in clearly different hydro-mechanical behavior. Particularly, prior to reactivation, reverse faults undergo <em>compaction</em> even at differential stresses well below the value required for reactivation. Contrarily, normal faults experience <em>dilation</em>, most of which occurs only near the differential stress values required for reactivation. Moreover, when reactivating at comparable normal stress, normal faults (load-weakening path) are more prone to slip seismically than reverse fault (load-strengthening path). Indeed, the higher mean stress that normal fault experienced before reactivation compacts more efficiently the gouge layer, thus increasing the fault stiffness and favoring seismic slip. This contrasting fault zone compaction and dilation prior to reactivation may occur in different natural tectonic settings, affecting the fault hydro-mechanical behavior. Thus, to take into account the loading path the fault experienced is fundamental in evaluating both natural and induced fault reactivation and the related seismic risk assessment.</p>


2014 ◽  
Vol 137 (1) ◽  
Author(s):  
Guian Qian ◽  
Markus Niffenegger

The integrity of a reactor pressure vessel (RPV) related to pressurized thermal shocks (PTSs) has been extensively studied. This paper introduces the method of using fracture mechanics for the integrity analysis of a RPV subjected to PTS transients. A 3-D finite element (FE) model is used to perform thermal and fracture mechanics analyses by considering both elastic and elastic–plastic material models. The results show that the linear elastic analysis leads to a more conservative result than the elastic–plastic analysis. The variation of the T-stress and Q-stress (crack tip constraint loss) of a surface crack in a RPV subjected to PTSs is studied. A shallow crack is assumed in the RPV and the corresponding constraint effect on fracture toughness of the material is quantified by the K–T method. The safety margin of the RPV is larger based on the K–T approach than based only on the K approach. The J–Q method with the modified boundary layer formulation (MBL) is used for the crack tip constraint analysis by considering elastic–plastic material properties. For all transient times, the real stress is lower than that calculated from small scale yielding (SSY) due to the loss of crack tip constraint.


Author(s):  
Zhongxian Wang ◽  
Yan-qing Zhang ◽  
Poh-Sang Lam ◽  
Yuh J. Chao

Typical pressure vessels are subject to biaxial loading. Creep analysis was conducted with two-dimensional finite element method for a center-cracked plate under a range of biaxial loading ratios (λ = −1, 0, and 0.5). The effects of crack size and the biaxial loading ratio on the crack tip field are reported. In addition, based on a two-parameter fracture theory, C(t)−A2(t), where C is a contour integral and is path-independent when the steady state creep is reached (denoted by C*), and A2 is a time dependent crack tip constraint parameter. The crack tip stress field calculated from the C(t)−A2(t) theory is shown to be more accurate than the Hutchinson–Rice–Rosengren (HRR) singularity solution, especially in the case of λ = 0.5. The loading level appears to have little effects on the constraint parameter A2(t). As creep time increases, the creep zone (based on the equivalent creep strain) increases rapidly but the yield zone (with respect to a reference stress) decreases. Meanwhile, the crack tip constraint is increasing with creep time, particularly for the small cracks. It was also found that the normalized relationship between the contour integral C(t)/C* and the creep time t/tT (where tT is the characteristic time for transition from small-scale creep to extensive creep) is insensitive to the biaxial loading. Therefore, the relationship previously provided for uniaxial loading can be used for biaxial loading.


Author(s):  
David W. Beardsmore

When crack tip constraint is high, the crack tip contour integral J characterises the asymptotic stress, strain and displacement fields of a stationary crack in an elastic-plastic material. In other cases, the crack tip fields can be related to J and a second parameter Q which governs the crack tip constraint. These observations are the basis of J-Q fracture mechanics assessments. In the most usual procedure J is compared to an effective, constraint-corrected fracture toughness Jc which is derived from Q and the fracture toughness of the material. The difference Jc – J is a measure of the margin of safety. The assessment procedure assumes there are no initial inelastic strains in the component or the fracture toughness specimen prior to introducing the crack and subsequent loading. However, plant components may contain inelastic strains prior to cracking arising from welding and other manufacturing or fit-up processes. This initial strain field can be established by a finite element analysis that simulates the welding and/or manufacture sequence. Weld residual stresses develop due to the accumulation of incompatible, inelastic strains, including thermal, plastic and transformation strains in the material. If a crack is inserted into an initial strain field, a procedure is required to calculate J by analysis of the resulting crack tip fields. Moreover, for the fracture assessment method to remain valid, it must be demonstrated that the values of J and Q continue to govern the onset of crack extension or fracture so that a meaningful comparison of J with Jc can be made. This paper describes a domain integral for calculating J when inelastic strains exist prior to cracking, and its implementation in the JEDI computer code. The code is used to determine J for a crack inserted into a three-point bend specimen containing an initial inelastic strain field representative of one that might develop during welding. The extent to which the crack tip stress field is characterised by J and Q is examined by comparing it to the field for high constraint, small-scale yielding conditions.


Author(s):  
Yuh J. Chao ◽  
Xian-Kui Zhu ◽  
Yil Kim ◽  
M. J. Pechersky ◽  
M. J. Morgan ◽  
...  

Because crack-tip fields of single edge notched bend (SENB) specimens are significantly affected by the global bending moment under the conditions of large-scale yielding (LSY), the classical crack tip asymptotic solutions fail to describe the crack-tip fields within the crack tip region prone to ductile fracture. As a result, existing theories do not quantify correctly the crack-tip constraint in such specimens under LSY conditions. To solve this problem, the J-A2 three-term solution is modified in this paper by introducing an additional term derived from the global bending moment in the SENB specimens. The J-integral represents the intensity of applied loading, A2 describes the crack-tip constraint level, and the additional term characterizes the effect of the global bending moment on the crack-tip fields of the SENB specimens. The global bending stress is derived from the strength theory of materials, and proportional to the applied bending moment and the inverse of the ligament size. Results show that the global bending stress near the crack tip of SENB specimens is very small compared to the J-A2 three-term solution under small-scale yielding (SSY), but becomes significant under the conditions of LSY or fully plastic deformation. The modified J-A2 solutions match well with the finite element results for the SENB specimens at all deformation levels ranging from SSY to LSY, and therefore can effectively model the effect of the global bending stress on the crack-tip fields. Consequently, the crack-tip constraint of such bending specimens can now be quantified correctly.


1976 ◽  
Vol 98 (2) ◽  
pp. 146-151 ◽  
Author(s):  
D. M. Tracey

The subject considered is the stress and deformation fields in a cracked elastic-plastic power law hardening material under plane strain tensile loading. An incremental plasticity finite element formulation is developed for accurate analysis of the complete field problem including the extensively deformed near tip region, the elastic-plastic region, and the remote elastic region. The formulation has general applicability and was used to solve the small scale yielding problem for a set of material hardening exponents. Distributions of stress, strain, and crack opening displacement at the crack tip and through the elastic-plastic zone are presented as a function of the elastic stress intensity factor and material properties.


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