Crack Line Analysis Method Research Articles

Analytical analysis on the Dugdale model of a finite-width cracked plate by using crack line analysis method

The Dugdale model is one of the most famous achievements in fracture mechanics due to its accurate predication of the size of the plastic zone at the crack tip in comparison with the experimental results. However, the Dugdale model is generally used for the analysis of infinite-width cracked plates, and it has not been successfully extended analytically for the analysis of finite-width cracked plates, which are more commonly seen in engineering structures. In this paper, the Dugdale model of finite-width cracked plates was analytically analyzed based on the crack line analysis method. Solving the plastic zone of the Dugdale model of a finite-width plate with a mode-I center crack was broken down into two problems of finite-width plates, and the analytical solutions of stress intensity factors of the two problems were obtained, respectively. Based on the superposition principle of stress intensity factors, the size of the plastic zone of the Dugdale model of a finite-width plate with a mode-I center crack was obtained. The results are in perfect consistency with the experimental values obtained by Dugdale himself, and the difference between the theoretical curve and the experimental values obtained by Dugdale was eliminated for the first time.

Near Crack Line Elastic‐Plastic Field for Mode I Cracks under Plane Stress Condition in Rectangular Coordinates

By using the crack line analysis method, this paper carries out an elastic‐plastic analysis for mode I cracks under plane stress condition in an elastic perfectly plastic solid and obtains the general form of matching equations of the elastic stress field and the plastic stress field near the crack line in rectangular coordinate form. The analysis in rectangular coordinates in this paper avoids the conversion from rectangular coordinates into polar coordinates in the existing analysis and greatly simplifies the power series forms of the elastic stress field and plastic stress field near the crack line during the solving process. Furthermore, by focusing on a new problem, i.e., the center‐cracked plate with finite width under unidirectional uniform tension, this paper obtains the elastic stress field, plastic stress field, and the length of the elastic‐plastic boundary near the crack line by using the general form of the solution. When the dimensions of the plate tend to be infinite, the results of this paper are consistent with those obtained for an infinite plate with a mode I crack. Furthermore, the variation curves of the length of the elastic‐plastic boundary are also delineated in different sized center‐cracked plates, and the results are compared with those obtained under the small‐scale yielding conditions. The solving process and the results in this paper abandon the small‐scale yielding conditions completely. The method used in this paper not only makes the solving process simpler during the elastic‐plastic analysis near the crack line but also enriches the crack line analysis method.

裂纹面局部均布荷载下Ⅰ型裂纹有限宽板应力强度因子

With the crack line analysis method for stress intensity factors, the stress intensity factor of a finite-width plate with a mode-Ⅰ center crack subjected to uniform stress on the crack surface near the crack tip was studied analytically. Through analytical solution of the stress field and correction of the stress components on the crack line of an infinite-width plate with a mode-Ⅰ crack under uniform stress on the crack surface near the crack tip, the corrected stress components on the crack line of the corresponding finite-width plate were further deduced. Reasonable requirements on the corrected stress field at the crack line were proposed, the stress intensity factor of the finite-width plate was derived, and the correction coefficient of the stress intensity factor of the finite-width plate relative to the corresponding infinite-width plate was obtained. When the width of the finite-width plate approaches infinity, the stress intensity factor of the finite-width plate will be consistent with that of the corresponding infinite-width plate.

Elastic-plastic analysis of the crack surface vicinity under a pair of anti-plane forces applied at an arbitrary point on the crack surface

An elastic-plastic analysis of the mode III crack surface vicinity was performed in an infinitely wide elastic-perfectly plastic plate, in which a pair of anti-plane forces applied at an arbitrary point on the crack surface. The crack line analysis method was used without the traditional small-scale yield condition. The plastic zone length, the plastic zone shape, and the elastic-plastic stress field in the vicinity of the crack surface were obtained analytically. Moreover, the plastic zone lengths in the vicinity of the crack surface and crack line were compared, and it was found that under a pair of anti-plane forces applied at an arbitrary point on the crack surface, the plastic zone length in the vicinity of the crack surface reached its maximum faster than that in the vicinity of the crack line under the same conditions, which indicates the stress state near the crack surface region is more detrimental than that near the crack line region. The variation of plastic zone length with the load position was also studied, and it was shown that when the point forces were closer to the crack tip, the plastic zone length was smaller and the stress state of the crack was more disadvantageous.

Elastic-plastic analysis near the crack surface region on a mode III crack under a pair of point forces

The crack line analysis method is used to obtain the near-crack-surface stress field of a mode III crack loaded by a pair of anti-plane point forces in an elastic-perfectly plastic material, which expands the research method from the crack line region to the crack surface region. The stresses in the plastic region, the length of the plastic region, and the geometry of the elastic-plastic boundary near the surface area of the crack are obtained analytically. Further, the maximum value of size of the plastic region along the surface of the crack is obtained. The results are sufficiently precise near the surface area of the crack, as the usual small-scale yielding condition has been given up in the analysis.

Elastic-plastic analysis of antiplane crack near crack surface region

The elastic-plastic stress distribution and the elastic-plastic boundary configuration near a crack surface region are significant but hard to obtain by means of the conventional analysis. A crack line analysis method is developed in this paper by considering the crack surface as an extension of the crack line. The stresses in the plastic zone, the length, and the unit normal vector of the elastic-plastic boundary near a crack surface region are obtained for an antiplane crack in an elastic-perfectly plastic solid. The usual small scale yielding assumptions are not needed in the analysis.

Elastic–plastic near field solution of an eccentric crack under shear in a finite width plate

The near crack line analysis method is used to investigate an eccentric crack loaded by shear forces in a finite width plate, and the analytical solution is obtained in this paper. The solution includes: the unit normal vector of the elastic–plastic boundary near the crack line, the elastic–plastic stress fields near crack line, variations of the length of the plastic zone along the crack line with an external loads, and the bearing capacity of a finite plate with a centric crack loaded by shear stress in the far field. The results obtained in this paper are sufficiently precise near the crack line because the assumptions of small scale yielding theory have not been made and no other assumptions have been taken. Subsequently, the present results are compared with the traditional line elastic fracture mechanical solutions and elastoplastic near field solutions under small scale yielding condition. On the basis of the minimum strain energy density (SED) theory, the minimum values of SED in the vicinity of the crack tip are determined, the initial growth orientation of crack are determined. It is found that the normalized load under large scale yielding condition is higher than those under small scale yielding condition when the length of the plastic zone is the same.

General forms of elastic-plastic matching equations for mode-III cracks near crack line

Crack line analysis is an effective way to solve elastic-plastic crack problems. Application of the method does not need the traditional small-scale yielding conditions and can obtain sufficiently accurate solutions near the crack line. To address mode-III crack problems under the perfect elastic-plastic condition, matching procedures of the crack line analysis method are summarized and refined to give general forms and formulation steps of plastic field, elastic-plastic boundary, and elastic-plastic matching equations near the crack line. The research unifies mode-III crack problems under different conditions into a problem of determining four integral constants with four matching equations. An example is given to verify correctness, conciseness, and generality of the procedure.

Elastoplastic solution for an eccentric crack loaded by two pairs of point tensile forces

The strain energy density theory and the near crack line analysis method are applied to investigate an eccentric crack loaded by two pairs of tensile point forces in a finite plate. The minimum values of SED in the vicinity of the crack tip are determined, the initial growth orientation of crack are determined. Obtained is the elastic–plastic solution near the crack line of an eccentric crack loaded by two pairs of point tensile forces under large scale yielding condition. More specifically, the near field solution contains the unit normal vector of the elastic–plastic boundary and the elastic–plastic stress field. The length of the plastic zone along the crack line is found to vary with the external load and the bearing capacity of a finite plate with an eccentric crack loaded by two pairs of tensile point forces. Compared with small scale yielding condition, the normalized load obtained is higher than those under small scale yielding condition when the length of the plastic zone is the same.

Elastic-plastic analytical solution for centric crack loaded by two pairs of point shear forces in finite plate

The near crack line analysis method was used to investigate a centric crack loaded by two pairs of point shear forces in a finite plate, and the analytical solution was obtained. The solution includes the unit normal vector of the elastic-plastic boundary near the crack line, the elastic-plastic stress fields near the crack line, the variations of the length of the plastic zone along the crack line with an external load, and the bearing capacity of a finite plate with a centric crack loaded by two pairs of point shear forces. The results are sufficiently precise near the crack line because the assumptions of small scale yielding theory have not been made and no other assumptions are taken.

Elastoplastic analysis for infinite plate with centric crack loaded by two pairs of point shear forces

The near crack line analysis method was used to investigate a crack loaded by two pairs of point shear forces in an infinite plate in an elastic-perfectly plastic solid, and the analytical solution was obtained. The solutions include: the unit normal vector of the elastic-plastic boundary near the crack line, the elastic-plastic stress fields near crack line, law that the length of the plastic zone along the crack line is varied with an external loads, and the bearing capacity of an infinite plate with a center crack loaded by two pairs of point shear forces. The results are sufficiently precise near the crack line because the assumptions of the small scale yielding theory have not been made and no other assumption have been taken.

Study on the coalescence mechanism of splitting failure of crack-weakened rock subjected to compressive loads

It is of important significance to study the coalescence mechanism of splitting failure of crack-weakened rock masses under compressive loads. In this paper, a simplified mechanism of crack propagation, in which the crack grows along the direction of maximum principal compressive stress, is proposed. Thus, only mode I is taken into account in the formulation and solution. On the basis of the near crack line analysis method, the elastic–plastic stress field near the crack line is analyzed, and the law that the length of the plastic zone along the crack line is varied with an external loads have been established by the matching condition of the elastic- plastic fields on the boundary, the coalescence stress and the strength properties of rock masses have been determined. The solution is a function of the geometry of the crack array. The results show that the crack coalescence depends on the crack interface friction coefficient, the sliding crack spacing, orientation of the cracks, and the crack half-length. The conclusions are of important significance for rock mass engineering.

Near crack line elastic–plastic analysis for a infinite plate loaded by two pairs of point tensile forces

The near crack line analysis method is used to investigate a center crack loaded by two pairs of point tensile forces in an infinite plate in an elastic–perfectly plastic solid, and the analytical solutions are obtained in this paper. These solutions include: the elastic–plastic stress field near the crack line, the law that the length of the plastic zone along the crack line is varied with an external loads and the bearing capacity of an infinite plate with a center crack. The results of this paper are sufficiently precise near the crack line because the assumptions of the small scale yielding theory have not been used and no other assumptions have been taken.

Elastic-plastic analytical solutions for an eccentric crack loaded by two pairs of anti-plane point forces

The improved near crack line analysis method was used to investigate an eccentric cracked plate loaded by two pairs of anti-plane point forces at the crack surface in an elastic-perfectly plastic solid. The analytical solutions of the elastic-plastic stress fields and displacements near the crack line have been found without the assumptions of the small scale yielding. The law that the length of the plastic zone along the crack line is varied with an external loads and the bearing capacity of an eccentric cracked plate are obtained.

General form of matching equation of elastic-plastic field near crack line for mode I crack under plane stress condition

Crack line field analysis method has become an independent method for crack elastic-plastic analysis, which greatly simplifies the complexity of crack elastic-plastic problems and overcomes the corresponding mathematical difficulty. With this method, the precise elastic-plastic solutions near crack lines for variety of crack problems can be obtained. But up to now all solutions obtained by this method were for different concrete problems, no general steps and no general form of matching equations near crack line are given out. With crack line analysis method, this paper proposes the general steps of elastic-plastic analysis near crack line for mode I crack in elastic-perfectly plastic solids under plane stress condition, and in turn given out the solving process and result for a specific problem.

Near crack line elastic-plastic analysis for a finite plate loaded by two pairs of antiplane point forces

In this paper, the improved near crack line analysis method proposed in Refs. [1] and [2] is used to investigate a center crack loaded by two pairs of antiplane point forces in a finite plate in an elastic-perfectly plastic solid. And the analytical solutions are obtained, that is elastic-plastic stress fields near the crack line and the law that the length of the plastic zone along the crack line is varied with an external loads and the bearing capacity of a finite plate with a center crack. The results of this paper are sufficiently precise near the crack line because the assumptions of the small scale yielding theory have not been used and no other assumptions have been taken.

Near crack line elastic-plastic analysis for a crack loaded by antiplane point forces

In this paper, the improved near crack line analysis method proposed in Refs. [1] and [2] is used to investigate a mode III crack loaded by antiplane point forces in an infinite plate in an elastic-perfectly plastic solid. The solutions of this paper are sufficiently precise near the crack line region because the assumptions of the small scale yielding theory have not been used and no other assumptions have been taken.

Exact solutions of near crack line fields for mode I crack under plane stress condition in an elastic-perfectly plastic solid

The near crack line analysis method has been used in the present paper. The classical small scale yielding conditions have been completely abandoned in the analyses and one inappropriate matching condition used to be used at the elasticplastic boundary has been corrected. The reasonable solution of the plastic stresses near the crack line region has been established. By matching the plastic stresses with the exact elastic stresses at the elastic-plastic boundary, the plastic stresses, the length of the plastic zone and the unit normal vector of the elastic-plastic boundary near the crack line region have been obtained for a mode I crack under uniaxial tension, as well as a mode I crack under biaxial tension, which shows that for both conditions the plastic stress components σv and σ2v, the length of the plastic zone and the unit normal vector of the elastic-plastic boundary are quite the same while the plastic stress σx is different.

Precise elastic-plastic analysis of crack line field for mode II plane strain crack

The near crack line analysis method has been used to investigate the exact elastic-plastic solutions of a mode II crack under plane strain condition in an elastic-perfectly plastic solid. The significance of this paper is that the assumptions of the conventional small scale yielding theory have been completely abandoned. The inappropriateness of matching conditions formerly taken at the elastic-plastic boundary ths been corrected as well. By eatching the general solution of the plastic stress (but not the special solution that was adopted) with the exact elastic stresses (but not the crack tip K-dominant field) at the elastic-plastic boundary near the crack line, the plastic stresses, the length of the plastic zone and the unit normal vector of the elastic-plastic boundary, which are sufficiently precise near the crack line region, have been given. The solutions are suitable not only under the condition that the plastic region is sufficiently small but also under the condition that the plastic region is large.

Elastic-plastic crack line fields for a growing crack in a centre cracked plate with finite dimensions

By using the near crack line analysis method, a cracked plate with finite dimensions can be easily analysed