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铝合金板材中心孔裂纹尖端塑性区数值计算

Numerical Calculation on Plastic Zone in Crack Tip of Central Hole of Aluminum Sheets
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摘要 通过有限元对铝合金板材中心孔裂纹尖端处塑性区模拟计算,说明在裂纹尖端产生了较大的塑性区,并相应地计算出塑性区的大小。本文通过有限元模拟2124铝合金板材中心孔裂纹扩展情况。铝合金材料为典型的脆性材料,2124铝合金板材在疲劳加载情况下会先进行弹性形变,达到屈服强度后进行塑性形变。本文对2124铝合金板材进行有限元模拟时,先采用线弹性模型,计算裂纹扩展的应力强度因子,然后采用弹塑性模型,计算裂纹尖端的塑性区大小,从而进一步对裂纹尖端应力强度因子进行修正。在建立有限元模型时,以二维的Ramberg-Os-good(R-O)本构为基础,采用参数化的方式,这样是为了可以更好地对有限元程序进行调试。在有限元网格划分时,由于在相同精度下四边形单元的计算效率是三角形单元的几倍,所以采用四边形单元,提高计算精度。有限元建模时,采用plane42、solid 45和solid 95三种单元,plane42单元用于建立2D网格,solid45单元用于建立3D网格,而solid95单元则是用于引入奇异单元。同时,由于试样模型对称性,所以取1/4模型来进行计算。在计算裂纹尖端应力强度因子及塑性区大小时,采用恒ΔK方式和增ΔK两种加载方式来进行计算。首先在恒ΔK下,计算出相应的应力强度因子,其值和理论值相吻合,同时观察得到的塑性区形状与理论形状相似,计算塑性区尺寸大小,首先证明有限元程序的正确性。进一步有限元模拟计算在增大ΔK情况下不同预裂纹长度下塑性区的变化情况。经过有限元计算得到的塑性区尺寸大小,最后可以近似用经验公式表达。 The intention of the text is to calculate the plastic zone in the crack tip of the central hole of aluminum sheets by finite element method.It demonstrates that there is a big plastic zone in the crack tip.The text mainly simulates the crack propagation of 2124 aluminum with a central hole.Because the aluminum alloy materials are typical brittle materials,the aluminum sheets are going to be elastic deformation firstly,then get to yield strength and go into plastic deformation.When I simulate the crack propagation of aluminum,firstly,I use liner elastic model and calculate the stress intensify factor.Second,I use elastic-plastic model and calculate the plastic zone,then modify the stress intensify factor.When building the finite element model,I make two-dimensional Ramberg-Osgood(R-O) constitutive as the foundation.At the same time,in order to better debugging the finite element program,the text adopts parameterized way.During mesh division,the effective of quadrilateral unit is several times of triangular unit in the same precision.When making a finite element model,I use plane42、solid45 and solid95 units,and plane42 is used to establish 2D grid,solid45 is used to establish 3D grid,and solid95 is used to introduce singular unit.Because of the symmetry of sample,the text just simulates 1/4 of the sample.The text calculates the stress intensify factor in two different conditions: constant ΔK and increasing ΔK and the result of text is coincide with theoretical results.Meanwhile the shape and size of plastic zone is similar to theoretical results,which shows that the finite element method is reasonable.Furthermore,the text simulates the crack propagation in different pre-crack length in constant ΔK and increasing ΔK by finite element method(FEM).Then the text put forward an experiential formula of plastic zone to crack propagation.
出处 《工程与试验》 2011年第3期12-15,共4页 Engineering and Test
关键词 裂纹扩展速率 塑性区半径 应力强度因子 fatigue crack growth propagation plastic zone stress intensify factor
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