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试验中选用的基板为45#钢,试验前用无水乙醇和丙酮清洗基板并风干,去除其表面的油污及杂质。LMD选用的粉末为高性能合金钢12CrNi2,其组分如表 1所示。粉末粒径为50μm~150μm,在扫描电子显微镜(scanning electron microscope,SEM)下观察粉末形貌,如图 1所示。试验前将粉末置于120℃真空保温箱中大约2h进行干燥处理,以去除粉末中的水分。
Table 1. Chemical composition of 12CrNi2 powder (mass fraction)
element Fe Ni Cr Mn Si C O content balance 0.016 0.0099 0.0056 0.0033 0.0012 0.00008 试验中选用4000W光纤激光器、以及同轴送粉装置构成的LMD试验系统,如图 2所示。制备过程的工艺参量如表 2所示,试验中使用稀有气体氩气作为保护气体。试验结束待试样冷却至室温后对试样进行表面无损检测确保其表面无裂纹,如图 3所示。为了避免打印过程中不同试样之间产生影响,每个试样选用一个独立的基板,打印完成后疲劳试样取样示意图如图 4所示。
Table 2. Process parameters of LMD
laser power spot diameter scanning speed power feeding rate overlap rate layer height 2200W 3mm 10mm/s 11g/s 50% 0.5mm -
试验中选用的CCT、CTS试样尺寸如图 5所示。采用INSTRON 8801试验机对试样施加应力比R=0.1、频率f=45Hz的正弦波循环载荷。CCT试样中载荷最大值F=15kN;CTS试样分两步加载,其中每步载荷最大值分别为F1=1.8kN,F2=3.8kN。试验过程中,使用采样摄像头对疲劳裂纹的扩展过程进行记录。每当裂纹向前扩展0.5mm时记录一次疲劳循环次数和裂纹形态,最终得到试样疲劳裂纹扩展的a-N曲线(其中a为裂纹长度,N为载荷循环次数)。
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材料弹性模量E=210GPa,泊松比μ=0.3[19]。由于试样厚度均远小于试样的长度和宽度且施加的载荷和约束在厚度方向上没有变化,扩展试验时在表面上测量裂纹扩展长度,因此把模型简化为2维平面应力问题来处理。利用有限元软件ABAQUS,根据几何模型建立如图 6所示的有限元模型。选用4个节点单元CPS4R进行网格划分,裂纹扩展区的网格大小为0.20mm×0.20mm,网格敏感性会在后续讨论。CCT模型共有7160个节点和7072个单元;CTS模型共有12166个节点和11972个单元。
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直接循环分析可以较好地模拟材料在循环载荷作用下的过程。进行疲劳数值模拟时一般先计算开始部分载荷的响应,再根据经验公式计算后续载荷作用下的响应。
结合XFEM进行疲劳分析,当满足裂纹扩展条件时,程序会自动迭代计算裂纹前缘单元失效所需要最小的循环次数ΔN,此时该单元发生断裂。随着裂纹的扩展,裂纹速率满足Paris公式:
$ \frac{{{\rm{d}}\mathit{a}}}{{{\rm{d}}\mathit{N}}} = {\mathit{c}_3}{(\Delta \mathit{G})^{{\mathit{c}_4}}} $
(1) 而通过试验可以得到基于应力强度因子幅值的Paris公式:
$ \frac{{{\rm{d}}\mathit{a}}}{{{\rm{d}}\mathit{N}}} = C{(\Delta \mathit{K})^\mathit{m}} $
(2) 式中, da/dN为单次加载时的裂纹增长;a为裂纹长度;N为载荷循环次数;C, m, c3和c4为Paris模型参量;ΔK为应力强度因子幅值;ΔG为能量释放率幅值。
(1) 式和(2)式之间的换算关系,详见参考文献[20]。
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针对CCT试样试验所记录的裂纹扩展数据,采用自编译的MATLAB程序实现7点递增多项式方法求得了试验中的裂纹扩展速率,图 9所示为拟合得到材料的Paris公式。
此时Paris公式为:
$ \frac{{{\rm{d}}\mathit{a}}}{{{\rm{d}}\mathit{N}}} = {10^{ - 13.23}} \times {(\Delta \mathit{K})^{3.16}} $
(3) 即参量C=10-13.23,m=3.16。换算得到c3=1.53×10-5,c4=1.58,于是基于能量释放率形式的Paris公式为:
$ \frac{{{\rm{d}}\mathit{a}}}{{{\rm{d}}\mathit{N}}} = 1.53 \times {10^{ - 5}} \times {(\Delta \mathit{G})^{1.58}} $
(4) -
为了探究网格大小对模拟中裂纹扩展速率的影响,采用4种网格大小分别对CCT和CTS试样进行模拟分析探索,结果分别如图 10、图 11所示。由图中结果可以看出, 网格尺寸大小会影响裂纹扩展速率,是由于扩展有限元法计算裂纹扩展时每次会扩展一个一个的网格。根据试验结果和模拟结果对比,得到网格大小为0.20mm×0.20mm为最优,因此后续分析均基于此网格大小进行计算。
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CCT试样的试验和有限元得到的裂纹扩展路径均沿着水平方向,如图 12所示。根据Griffith准则[21],此时为Ⅰ型裂纹,裂纹沿着垂直于力的方向扩展。
图 13为CTS试样疲劳裂纹扩展路径的试验结果与有限元模拟结果。根据HUSSAIN提出的最大能量释放率准则(maximum energy release rate criterion, MERRC)[22],裂纹扩展方向为裂纹尖端附近区域的最大能量释放率的方向。由于CTS试样的几何结构和加载条件都是非对称的,所以在疲劳载荷的作用下为Ⅰ-Ⅱ复合型裂纹,裂纹在扩展过程中会发生偏转。图 14为有限元法和试验方法得到的裂纹扩展路径示意图。通过计算可以得到两个加载步下偏转角的误差分别为16.54%和13.45%,如表 3所示。计算的误差为有限元结果和试验结果的差值与试验结果的比值,由于step-1加载下的偏转角α1较小,所以导致在误差计算时出现较大误差的情况。
表 3 Deflection angle of fatigue crack growth
deflection angle specimen 1 specimen 2 XFEM error/% α1(step-1)/(°) 2.22 1.71 1.64 16.54 α2(step-2)/(°) 39.66 47.11 37.55 13.45 -
图 15、图 16分别为CCT、CTS试样疲劳裂纹扩展的a-N曲线。其中“specimen编号”分别对应不同编号的试验件,“left,right”分别为1#、2#试验件左、右两侧的数据;XFEM-CCT和XFEM-CTS为扩展有限元方法计算的疲劳裂纹扩展数据,采用的是最优网格尺寸0.20mm×0.20mm分析得到的结果。由图中结果可以得出,随着裂纹长度的不断增加,能量释放率幅值ΔG不断增加,从而导致裂纹扩展速率呈现增加的趋势。
疲劳寿命的试验结果和有限元模拟结果误差分析如表 4、表 5所示。由于CCT试验中的裂纹为Ⅰ型裂纹,裂纹始终沿着水平方向扩展,所以裂纹扩展较为稳定误差也较小;而CTS试样在疲劳载荷作用下为Ⅰ-Ⅱ复合型裂纹,裂纹扩展相较Ⅰ型裂纹稳定性变差,所以模拟的误差会稍大。上述误差分析结果表明,本文中预测的疲劳寿命与试验值具有很好的一致性。
Table 4. Fatigue life of CCT
type specimen 1 specimen 2 XFEM-CCT error/% fatigue life 461946 494774 480454 0.44 Table 5. Fatigue life of CTS
type specimen 3 specimen 4 XFEM-CTS error/% fatigue life(step-1) 318243 348685 324909 2.57 fatigue life(step-2) 461762 477800 456999 2.72
激光熔化沉积高合金钢疲劳裂纹扩展研究
Study on fatigue crack growth of laser melting deposited high alloy steel
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摘要: 为了研究激光熔化沉积高性能合金钢构件的疲劳问题,采用扩展有限元法和直接循环分析相结合的方法,进行了典型件疲劳裂纹扩展路径的分析, 并进行了剩余寿命的预测。通过中心裂纹拉伸(CCT)试样的疲劳试验获得了材料Paris公式中的参量,并将其用于有限元模拟中。同时,分别运用有限元模拟方法和试验方法研究了CCT、紧凑拉伸-剪切试样的裂纹扩展过程。结果表明, 有限元法得到的裂纹扩展路径和疲劳寿命与试验结果吻合良好,其中裂纹扩展路径偏转角的误差在16.54%以内,疲劳寿命的误差在2.72%以内。该方法可以较好地预测激光熔化沉积高合金钢构件的疲劳裂纹扩展路径和剩余疲劳寿命,具有一定的工程意义。Abstract: In order to study the fatigue problem of laser melting deposition(LMD) high alloy steel, the fatigue crack growth path and residual life prediction of typical samples were analyzed by the extended finite element method and the direct cyclic. The parameters in Paris formula were obtained by the fatigue experiment of center crack tension(CCT)specimen, and then were used in the finite element simulation. The crack growth process of CCT and compact tension shear samples was studied by the finite element simulation and the experiment respectively. The results indicate that the crack growth path and fatigue life obtained by the finite element simulation are in good agreement with the experiment data. The error of deflection angle of crack propagation path is less than 16.54%, and the error of fatigue life is less than 2.72%. The results show that this method can predict the fatigue crack growth path and fatigue life of LMD high alloy steel components well, which has a certain engineering sense and practice value.
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Table 1. Chemical composition of 12CrNi2 powder (mass fraction)
element Fe Ni Cr Mn Si C O content balance 0.016 0.0099 0.0056 0.0033 0.0012 0.00008 Table 2. Process parameters of LMD
laser power spot diameter scanning speed power feeding rate overlap rate layer height 2200W 3mm 10mm/s 11g/s 50% 0.5mm 表 3 Deflection angle of fatigue crack growth
deflection angle specimen 1 specimen 2 XFEM error/% α1(step-1)/(°) 2.22 1.71 1.64 16.54 α2(step-2)/(°) 39.66 47.11 37.55 13.45 Table 4. Fatigue life of CCT
type specimen 1 specimen 2 XFEM-CCT error/% fatigue life 461946 494774 480454 0.44 Table 5. Fatigue life of CTS
type specimen 3 specimen 4 XFEM-CTS error/% fatigue life(step-1) 318243 348685 324909 2.57 fatigue life(step-2) 461762 477800 456999 2.72 -
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