Effect of Formed Specimen Shape and Size on Residual Stress of Titanium Alloy Formed by Selective Laser Melting
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摘要:
以TC4钛合金粉末为原料,采用激光选区熔化（SLM）方法直接成形直径16 mm的柱状试样,平行段直径7 mm、夹持段直径16 mm的疲劳试样以及厚度分别为10,22 mm的板状试样等4种形状与尺寸的试样,采用轮廓法测试了试样的z向（成形方向）残余应力,分析了试样形状和尺寸对残余应力的影响。结果表明：SLM成形试样内部残余应力为压应力,表层为拉应力,残余压应力分布形状与试样切割截面形状类似,分别呈近圆形和近矩形；与22 mm厚板状试样相比,10 mm厚板状试样厚度方向中心线上的内部压应力分布跨度及幅值低,宽度方向中心线上的内部压应力分布跨度不变,压应力峰值降低近1/2。SLM成形试样的内部压应力分布和幅值受试样形状和尺寸的影响较大,归因于不同形状和尺寸试样成形时的拘束度不同。
Abstract:With TC4 titanium alloy powder as raw materials, four types of specimens with different shapes and sizes, including the columnar specimen with diameter of 16 mm, the fatigue specimen with diameter of 7 mm in parallel section and diameter of 16 mm in clamping section, the plate specimens with thickness of 10 mm and 22 mm were directly formed by selective laser melting (SLM) . The z-directional (forming direction) residual stress of the specimen was measured by the contour method. The effects of specimen shape and size on residual stress were analyzed. The results show that the internal residual stresses of SLM formed specimens were compressive stresses, and the surface residual stresses were tensile stresses. The distribution shape of residual compressive stresses was similar to the shape of the specimen cutting section, it was nearly circular and nearly rectangular, respectively. Compared with the 22 mm-thick plate specimen, the distribution span and amplitude of the internal compressive stress on the centerline in the thickness direction of the 10 mm-thick plate were lower, the distribution span of the internal compressive stress on the centerline in the width direction was unchanged, and the peak value of the compressive stress was reduced by nearly 1/2. The internal compressive stress distribution and amplitude of SLM formed specimen were greatly affected by the shape and size of the specimen, which was attributed to the different constraints in forming of specimens with different shapes and sizes.
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0. 引言
激光选区熔化（SLM）是一种重要的金属增材制造技术,该方法以激光为热源,选择性地使金属粉末快速熔化后凝固,并逐层堆积形成需要的零件。金属的快速熔化和凝固会造成零件内部显著的残余应力累积,导致成形零件出现大变形或开裂问题[1-2],从而降低零件的承载能力,影响其服役性能[3-4]。增材制造过程中残余应力的产生受工艺参数、支撑板的使用、成形件尺寸和形状等因素的影响[5]。在相同的材料和增材制造工艺条件下,直接成形的不同尺寸和形状试样的残余应力分布和幅值不同[6],这使得基于不同尺寸和形状的试样获得的力学性能结果也不同,从而影响对成形件的性能评价和预测。
目前,增材制造试样中应力分布特征的研究多集中在采用X射线衍射法测试块状试样表面一条线上的应力分布[5],或采用中子衍射法获得柱状试样一条直径线上的内部应力分布[6]等方面,少有对某一平面应力二维分布进行研究的报道。轮廓法[7]是一种经济高效、测试精度和空间分辨率均很高的破坏性残余应力测试方法,可获得可视化的构件截面残余应力二维分布。该测试方法主要包括工件切割、轮廓测量、数据处理和有限元建模计算4个步骤：将构件切割成两半释放内部残余应力,测量切割面轮廓获得因应力释放而导致的切割面变形数据,以变形数据为边界条件,采用有限元法构造切割面上的应力分布[8-11],得到切割前该平面的原始应力分布。轮廓法测试残余应力的准确性已得到X射线衍射[12]、中子衍射[13]、同步辐射X射线衍射[14]等测试方法和数值计算[15]的验证。
作者以TC4钛合金粉末为原料,采用SLM直接成形4种形状和尺寸的试样,基于轮廓法获得了试样内部残余应力分布,研究了试样形状和尺寸对残余应力的影响。研究成果可为SLM成形TC4钛合金构件的残余应力分析提供指导。
1. 试样制备与试验方法
试验原料为粒径约30 μm的TC4钛合金粉末,由德国TLS3D打印金属粉末制造公司提供。采用EOS-M280型商用SLM增材制造机通过选区激光熔化成形制备如图1所示的4种试样（z为成形方向）,工艺参数参考文献[16]确定：激光光斑直径为100 μm,激光功率为260~300 W,扫描速度为1 000~1 400 mm·s−1,扫描间距为0.14 mm,相邻层间扫描路径夹角为67°,相同层扫描时激光光斑搭接率为25%。
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图 1 SLM直接成形试样的形状与尺寸Figure 1. Shape and size of specimens directly formed by SLM: (a) columnar specimen; (b) fatigue specimen; (c) 10 mm-thick plate specimen and (d) 22 mm-thick plate specimen采用轮廓法测试应力：如图2所示,将试样夹持后,使用Seibu M50型慢走丝线切割机将其切割成两半,切割丝为直径0.25 mm的纯铜丝,切割速度约为1.0 mm·min−1,切割过程在去离子水中进行,以减小切割造成的热应力；采用蔡司PRISMO型三坐标测量仪测试切割面轮廓,扫描测试精度约为1.2 µm,轮廓数据经过剔除误差点、插值平均和光滑拟合后,作为有限元模拟的边界条件；按照切割后试样的有效尺寸数据建立有限元模型（见图3）,将光滑拟合的切割面变形数据作为位移边界条件施加到有限元模型的相应切割面节点上,经过弹性有限元计算,即可获得切割前切割面上的z向残余应力分布。在建立有限元模型时,考虑到切割面变形量小（约20 μm）以及为了建模和加载位移方便,将疲劳试样模型简化为直径7 mm的圆柱体。采用ANSYS软件的Solid185六面体划分单元,疲劳试样切割面网格尺寸为0.15 mm×0.15 mm,柱状试样切割面网格尺寸为0.4 mm×0.4 mm,两种板状试样切割面网格尺寸为0.5 mm×0.5 mm。柱状试样模型包含40 680个单元和43 183个节点,疲劳试样模型包含35 820个单元和38 388个节点；10 mm和22 mm厚板状试样模型的单元数分别为25 650个和45 150个,节点数分别为29 120和49 984个。材料的弹性模量和泊松比分别为105 GPa[16]和0.34[17]。
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图 2 不同试样的夹持及切割方式Figure 2. Clamping and cutting methods of different specimens: (a) columnar specimen; (b) fatigue specimen and (c) plate specimen![]()
图 3 对半切割后4种试样的有限元模型Figure 3. Finite element models of four kinds of specimens after cutting in half: (a) columnar specimen; (b) fatigue specimen; (c) 10 mm-thick plate specimen and (d) 22 mm-thick plate specimen2. 试验结果与讨论
2.1 柱状试样和疲劳试样的z向残余应力分布
由图4可以看出,柱状试样和疲劳试样的内部z向残余应力均为压应力,其分布形状基本呈圆形,与试样截面形状一致,表层z向残余应力为拉应力。这种内部为压应力表层为拉应力的分布特征与文献[6]的研究结果一致。在SLM增材制造过程中,试样边缘材料的散热快,收缩大,故试样内部会因受到边缘材料的压缩而形成压应力,表层则产生拉应力与之平衡。由图4还可以看出,试样切出端出现了高达2 000 MPa的拉应力,远远超过TC4钛合金的屈服强度（1 094 MPa）和抗拉强度（1 267 MPa）[16],这是由于轮廓法测试存在较大边缘误差。线切割时,切出端的材料迅速减少,影响切割参数的稳定性,后续表面轮廓测定时表层会产生较大位移误差[7,18-19],从而得到较高的表层应力值。
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图 4 柱状试样和疲劳试样切割面上的z向残余应力分布Figure 4. Distribution of z-directional residual stress on cutting surface of columnar (a) and fatigue (b) specimens将柱状试样和疲劳试样切割面直径线上的应力提取出来。由图5可见,两种试样的残余应力沿切割面直径线的分布曲线形状基本一致,直径较大的柱状试样的压应力峰值（690 MPa）大于直径较小的疲劳试样（493 MPa）,这与文献[6]采用中子衍射法测试SLM成形不同直径柱状试样的结果一致。
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图 5 柱状试样和疲劳试样切割面直径线上的z向残余应力分布曲线Figure 5. Distribution curves of z-directional residual stress along diameter line on cutting surface of columnar and fatigue specimens2.2 板状试样的z向残余应力分布
由图6可以看出：两种板状试样的内部z向残余应力均为压应力,表层则均为拉应力,内部压应力分布形状与其切割面形状相似,呈近矩形,与文献[17]采用轮廓法和数值模拟方法得到的SLM成形块状试样的应力分布一致；22 mm厚板状试样的压应力峰值达400 MPa左右,10 mm厚板状试样压应力峰值略低,为200 MPa左右；两种板状试样的边缘部分均出现较大幅值的拉应力,这是轮廓法的边缘测试误差造成的。22 mm厚试样切割初期出现了断丝现象,造成切入端约15 mm区域的变形数据失真,因此在数据处理和构建应力分布时舍弃了这部分数据（图6中虚线框出区域）,最终测试结果仍能反映内部应力分布。
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图 6 不同厚度板状试样切割面上的z向残余应力分布Figure 6. Distribution of z-directional residual stress on cutting surface of plate specimens with 10 mm thickness (a) and 22 mm thickness (b)提取板状试样切割面中心线上的残余应力。由图7（a）可以看出：两种板状试样y方向（厚度方向）中心线上的残余应力分布基本一致,表层均为拉应力,内部均为压应力；22 mm厚和10 mm厚板状试样内部压应力的分布跨度分别为15.5 mm（约为厚度的70%）和9 mm（为厚度的90%）；10 mm厚板状试样的压应力峰值（240 MPa）约为22 mm厚板状试样压应力峰值（约440 MPa）的1/2。可见,板状试样在厚度减薄后,y方向中心线上的压应力分布跨度和峰值均降低。由图7（b）可以看出,两种板状试样在x方向(宽度方向）中心线上的残余应力分布趋势基本一致,压应力分布跨度基本相同,10 mm厚板状试样的压应力峰值（220 MPa左右）约为22 mm厚板状试样压应力峰值（约420 MPa）的1/2,说明当SLM增材制造TC4钛合金板状试样宽度变化不大时,其厚度大小对内部x方向中心线上的压应力分布跨度没有影响,仅造成压应力幅值变化。
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图 7 不同厚度板状试样切割面不同方向中心线上的z向残余应力分布曲线Figure 7. Distribution curves of z-directional residual stress along different-directional centerline on cutting surface of plate specimens with different thicknesses: (a) y-direction and (b) x-direction试样内部残余压应力的分布形状与其切割面形状相似,这是试样的自拘束状态导致的。柱状试样各方向的自拘束度一致,形成了内部圆形压应力分布形式；板状试样的宽度和厚度尺寸不同,各方向的拘束度不一致,造成内部压应力和表层拉应力在这两个方向上的分布跨度均不一致。两种板状试样的宽度基本一致,因此x方向中心线上的压应力分布跨度基本一致；厚度差距较大,较小厚度试样y方向中心线上的压应力分布跨度较小。此外,直径较大柱状试样和厚度较大板状试样的拘束度大,因此内部压应力峰值大。综上可知,SLM直接成形试样的内部压应力分布及大小受试样形状及尺寸影响大,可归因于成形不同形状和尺寸试样时的拘束度不同。
3. 结论
（1）采用轮廓法测得SLM成形TC4钛合金试样的内部z向（成形方向）残余应力均为压应力,表层则为拉应力,内部压应力分布形状与切割面形状相似,柱状试样呈近圆形,板状试样呈近矩形。
（2）较大直径（16 mm）柱状试样切割面上的压应力幅值大于较小直径（7 mm）疲劳试样；与20 mm厚板状试样相比,10 mm厚板状试样的内部压应力在厚度方向中心线上的分布跨度和幅值降低,在宽度方向中心线上的分布跨度基本不变,但压应力峰值降低约1/2。内部压应力分布形状和幅值受试样形状和尺寸影响较大,可归因为不同形状和尺寸试样在成形过程中的拘束度不同。
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图 1 SLM直接成形试样的形状与尺寸
Figure 1. Shape and size of specimens directly formed by SLM: (a) columnar specimen; (b) fatigue specimen; (c) 10 mm-thick plate specimen and (d) 22 mm-thick plate specimen
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图 2 不同试样的夹持及切割方式
Figure 2. Clamping and cutting methods of different specimens: (a) columnar specimen; (b) fatigue specimen and (c) plate specimen
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图 3 对半切割后4种试样的有限元模型
Figure 3. Finite element models of four kinds of specimens after cutting in half: (a) columnar specimen; (b) fatigue specimen; (c) 10 mm-thick plate specimen and (d) 22 mm-thick plate specimen
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图 4 柱状试样和疲劳试样切割面上的z向残余应力分布
Figure 4. Distribution of z-directional residual stress on cutting surface of columnar (a) and fatigue (b) specimens
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图 5 柱状试样和疲劳试样切割面直径线上的z向残余应力分布曲线
Figure 5. Distribution curves of z-directional residual stress along diameter line on cutting surface of columnar and fatigue specimens
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图 6 不同厚度板状试样切割面上的z向残余应力分布
Figure 6. Distribution of z-directional residual stress on cutting surface of plate specimens with 10 mm thickness (a) and 22 mm thickness (b)
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