Mechanical behavior of additively manufactured AlSi10Mg alloy with annealing state under extreme conditions
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摘要: 采用激光选区熔化技术制备AlSi10Mg合金并对其进行去应力退火处理，利用光学显微镜、扫描电子显微镜和电子背散射衍射技术研究了合金的微观组织。为了解宽应变率和宽温度耦合作用对AlSi10Mg合金力学行为的影响，通过配有环境温箱的万能试验机和分离式霍普金森压杆分析了AlSi10Mg合金在极端条件下的力学行为。结果表明：AlSi10Mg合金具有精细的胞状-枝晶微观结构，主要包含α-Al相和Si相，经退火处理后，微观组织由断续的、呈链状分布的共晶Si颗粒构成。AlSi10Mg合金在室温、应变率为0.002～4 800 s−1时，呈现出应变率强化效应，且在不同的应变率范围内具有不同的敏感性；在173 K下具有更高的屈服强度和流动应力；当温度为173～243 K时，流动应力对温度不敏感；而温度为293～573 K时，温度敏感性显著提高，合金软化效应随着温度的升高而加剧。基于实验结果拟合得到修正的J-C本构模型并对其进行了验证，该模型可较好地反映材料在高、低温和不同应变率下的力学行为。
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关键词:
- 激光选区熔化 /
- AlSi10Mg合金 /
- 微观组织 /
- 力学行为 /
- 修正的J-C本构模型
Abstract: In this study, AlSi10Mg alloy was prepared by selective laser melting (SLM) first, and then subjected to stress relieved annealing treatment. The microstructures of the alloy were analyzed by optical microscope (OM), scanning electron microscope (SEM) and electron backscatter diffraction (EBSD) technology. To understand the influence of coupling effects on the mechanical behavior of AlSi10Mg alloy under wide strain rates and wide temperatures, the mechanical behavior of the alloy under extreme conditions (high and low temperatures, high strain-rate) were analyzed by universal testing machine with an environmental chamber and split Hopkinson pressure bar. The results show that AlSi10Mg alloy possesses fine cellular dendritic microstructure, mainly including α-Al and Si phases, and annealing treatment can result in the discontinuous distribution of eutectic Si particles. AlSi10Mg alloy displays strain-rate strengthening effect under room temperature condition at 0.002–4 800 s−1, and has different strain-rate sensitivity in different strain-rate ranges. The material has higher yield strength and flow stress at 173 K. When the strain-rate is 0.002 s−1, the SLM AlSi10Mg alloy has different temperature sensitivities in different temperature ranges. The alloy does not have temperature sensitivity in the range of 173–243 K; the material exhibits temperature sensitivity ranging from 293 K to 573 K, and the softening effect due to temperature on the material intensifies with increasing temperature. Based on the J-C constitutive model, a modified J-C constitutive model expressed by piecewise functions is constructed and the experimental results are fitted. In addition, experimental verification was conducted on the modified J-C constitutive model, and the predicted results are basically consistent with the experimental results. Within the scope of the study, the modified J-C constitutive model effectively reflects the mechanical behavior of the alloy at high and low temperatures and under different strain-rate. -
镁合金是一种潜力巨大的轻质工程材料，有着广阔的应用前景，其中MB2是镁合金的典型代表。材料在复杂应力状态下的失效破坏行为是工程材料和结构设计的理论基础。目前，镁合金在动静态加载下的力学行为研究以单向应力状态为主[1-3]，且能实现复杂应力动态加载的实验设备与技术尚不成熟。J.W.Hancock等[4]研究发现金属的延性明显依赖于应力的三轴状态。近年来，O.S.Hopperstad等[5-6]对结构钢进行了拉伸加载实验和数值分析，结果表明材料的等效破坏应变随应力三轴状态的变化趋势与J.W.Hancock等的研究结论一致；Y.B.Bao[7]在单轴加载条件下对铝合金2024进行了不同应力状态的实验研究；D.Anderson等[8]研究了应力三轴度和应变率对DP780钢破坏行为的影响。汤安民等[9]、李智慧等[10]研究了不同金属材料宏观断裂形式及断裂机理与应力状态的关系, 陈刚等[11]建立了应力三轴度和应变率相关的45钢损伤失效模型, 朱浩等[12]分析了应力三轴度和应变率对铝合金6063力学性能的影响, 张伟等[13]以应力三轴度和应变率效应为基础给出了铝合金7A04的本构关系和失效模型。
所以，对于钢材、铝合金等常用金属材料，其失效破坏行为的研究已经很多，而对镁合金复杂应力状态下的失效破坏行为研究还很少。本文中将通过复杂应力下的动静态拉伸实验及数值模拟，分析应力状态和应变率对镁合金MB2失效破坏的影响，基于Johnson-Cook本构及失效模型建立适用于镁合金MB2的破坏准则，分析其宏观破坏模式及其微观失效机理，为镁合金MB2在实际工程中的应用提供强度设计依据和理论支撑。
1. 动静态拉伸实验方法
材料所受应力状态不同时，材料内产生的塑性变形与应力集中程度将不同，为了表征材料的复杂应力状态，引用应力三轴度η为应力状态参数，即平均应力与等效应力的比值σH/σ。在延性金属复杂应力状态的失效破坏研究中，依据Bridgman原理[14]设计的缺口试件拉伸实验是最主要的研究方法，根据圆弧缺口颈部应力方程解，可以得到应力三轴度的计算公式：
η=13+ln(1+a2−r22aR) (1) 式中：a和R分别为最小横截面的半径及缺口半径，r为到横截面中心的距离，a0为最小横截面初始半径。基于塑性不可压的假设，可以得到缺口处的等效应变定义公式如下：
ˉε=2ln(a0/a) (2) 当a取试件断裂时的横截面直径af时，式(2)计算得到的即为试件的等效破坏应变εf。静态拉伸实验试件采用直径为5 mm的光滑圆柱以及最小横截面直径为6 mm，缺口曲率半径分别为9、6、3 mm的缺口圆柱试件。动态拉伸实验试件采用直径为3 mm的光滑圆柱以及最小横截面直径为2 mm，缺口曲率半径分别为1.0、1.5、2.0、3.0 mm的缺口圆柱试件。静态拉伸加载由材料试验机MTS 810完成，而动态拉伸加载则通过分离式Hopkinson拉杆(SHTB)实验装置完成，如图 1所示。
2. 镁合金MB2的动静态本构关系
2.1 应变率及绝热效应
对于光滑圆柱试件的动态拉伸实验，按照一维应力波理论进行数据处理分析可知，试件在不同应力幅值的入射波作用下表现出了明显的应变率效应，不同应变率下的真实应力应变曲线如图 2所示。
在高速冲击载荷作用下，加载过程为绝热过程，材料在该过程中的温度变化ΔT可由塑性变形进行求解：
ΔT=βρcp∫εp0σdεp (3) 式中：β为摩擦能量转换系数，ρ为材料密度，cp为比定压热容，εp为等效塑性应变。对于镁合金MB2，摩擦能量转换系数通常取为0.925，密度为1 800 kg/m3，比定压热容为1 040~1 148 J/(kg·K)。
2.2 本构模型参数拟合
鉴于镁合金MB2的应变率效应，这里引用经典的J-C本构模型对实验结果进行拟合。在室温、准静态(0.001 s-1)拉伸条件下，J-C本构模型的应变率项和温度项均为1，此时材料的本构模型退化为：
σ=A+Bεnp (4) 采用最小二乘法对参数A、B、n进行拟合可以得到：A=192 MPa、B=218.3 MPa、n=0.370 56。由于在300 s-1下试件未被拉断，所以这里以800和1 800 s-1应变率下的抗拉强度及其对应的等效塑性应变作为比较点与参考应变率0.001 s-1进行比较分析，获得参数C的算术平均值为0.015。对于反映温度效应的参数m，由于本研究未涉及高温下的动态拉伸实验，所以此处引用文献[15]中的研究结论，给出参数m的值为0.95。
3. 失效破坏行为
3.1 宏观失效破坏
对于光滑圆柱试件和缺口圆柱试件，由于其加载过程中应力状态的差异，导致其动静态加载条件下的破坏形式也有所不同，如图 3所示。
光滑圆柱试件在整体上发生剪切破坏，且在破坏前有一定的颈缩，试件断口处有一定的杯锥特征。缺口试件在准静态条件下整体上发生正拉断，断口边缘有杯锥特征；在动态加载下整体表现为杯锥形断裂。通过测量断裂后缺口处的最小横截面直径，得到了动态拉伸试件不同加载条件下的等效破坏应变，如表 1所示。
表 1 不同类型试件的等效破坏应变Table 1. Equivalent fracture strain of different specimens入射波幅值/MPa 等效破坏应变 光滑 R=3.0 mm R=2.0 mm R=1.5 mm R=1.0 mm 50 未断裂 0.333 8 0.250 2 0.254 1 0.205 3 120 0.311 7 0.307 1 0.225 7 0.239 7 0.197 7 350 0.289 3 0.249 2 0.180 0 0.175 8 0.177 6 3.2 J-C失效模型
J-C失效模型类似于J-C本构模型，采用多项乘积的形式对应力状态参数、应变率参数以及温度效应参数进行解耦。由于在本研究中未涉及等效破坏应变的温度效应，所以此处给出简化后的表达形式如下：
ˉεf=[D1+D2exp(D3η)][1+D4ln(˙ε/˙ε0)] (5) 式中：D1、D2、D3、D4为失效模型系数。研究发现，试件最小横截面处的应力三轴度是随等效应变的增加而不断变化的，整个加载过程的应力三轴度计算需要考虑到应变的累积效应[16]，所以D.M.Goto等[17]、Y.Bao等[18]在研究不同延性金属材料时，对整个加载过程的平均应力三轴度ηav进行了定义：
ηav=1ˉεf∫ˉεf0η(ˉε)dˉε (6) 采用ABAQUS/Explicit分析软件对镁合金MB2不同类型试件的动态拉伸实验过程进行模拟计算，鉴于SHTB和试件的对称性，以轴对称单元进行建模，以拉伸本构关系和实验中采集的入射波为输入条件，模拟得到了试件在加载过程中应力三轴度的变化情况，如图 4所示。
同时，由于缺口试件动态加载过程中，其塑性变形集中于缺口区域，并不满足一维应力波原理，无法通过理论公式对应变率进行求解。所以这里根据缺口试件等效应变的定义，借助数值模拟得到最小横截面直径的变化和应力波作用时程，通过时间积分得到试件的平均应变率：
˙εav=1Δt∫tft0˙ε(t)dt=2Δtln(a0af) (7) 式中：Δt为试件发生拉伸变形的时间，t0为载荷作用开始的时刻，tf为载荷作用结束的时刻。通过数值计算得到不同类型试件入射波在试件上的作用时间，进而计算得到其平均应变率，如表 2所示。
表 2 缺口试件的平均应变率Table 2. Average strain rates of different specimens入射波幅值/MPa 平均应变率/s-1 R=3 mm R=2 mm R=1.5 mm R=1 mm 50 828 968 1 047 1 239 120 2 315 2 573 2 569 2 694 350 3 905 4 129 4 914 4 981 在准静态(˙ε=˙ε0)拉伸条件下，J-C失效模型的应变率项为1，且镁合金MB2的等效破坏应变存在明显的转折点[19]，通过拟合得到，应力三轴度小于0.66时，参数D1、D2、D3的值分别为1.04×10-5、0.073 7以及0.323；当应力三轴度大于0.66时，其值分别为105.7、-0.103以及0.236。对于镁合金MB2，J-C失效模型中的(εf/ε0-1)与ln(˙ε/˙ε0)并不满足线性关系，所以这里对模型中的应变率项进行了修正，修正后的失效模型为：
ˉεf=[D1+D2exp(D3η)]{1+D5 [ 1-exp(D6ln(˙ε/˙ε0))]} (8) 式中：D5、D6为应变率项参数。通过拟合分析发现，修正模型中(εf/ε0-1)与ln(˙ε/˙ε0)的关系与实验数据吻合，D5、D6的值分别为8.87×10-20、2.801，如图 5所示。
结合参数拟合的结果，可以得到镁合金MB2最终的破坏准则为以应力三轴度0.66为转折点的分段函数形式，如图 6所示。图中实心圆点为实验结果，曲面为破坏准则的拟合结果。
通过失效破坏曲面可以发现，镁合金MB2的断裂延性(等效破坏应变)随着应力三轴度的增加先增大后减小，随着应变率的增大而不断减小。从破坏模式上来看，随着应力三轴度的增大，材料先发生剪切破坏，随后又发生正拉断破坏；随着应变率的增大，光滑圆柱及缺口圆柱试件在动静态载荷作用下的破坏形式基本一致。所以，应力状态对断裂延性和破坏模式的影响存在明显的转折点，而应变率的影响则不存在转折点。
为了对该失效模型进行验证，这里通过ABAQUS/Explicit分析软件和单元失效法对不同类型试件的动态失效破坏形式进行了数值模拟分析，其模拟结果如图 7所示。
图 7 不同试件失效破坏模式的数值模拟结果Figure 7. Fracture patterns of different specimens from numerical simulation从数值模拟结果可以看出，无论是光滑圆柱试件还是缺口圆柱试件，其最终破坏形式均呈现出杯锥形特征，这与实验现象是基本吻合的；但对于光滑圆柱试件，该模型不能体现试件的整体剪切断裂特征，这与J-C失效模型的物理涵义以及镁合金MB2在不同应力状态下的微观损伤机理有关。
3.3 微观失效机理
宏观破坏行为与材料的微观损伤变形机制密切相关，为进一步认识应力状态对镁合金MB2破坏行为的影响，对准静态条件下光滑圆柱及缺口试件的断口形貌进行微观扫描观察，如图 8所示。
对于光滑拉伸试件，微观断口上能看到河流花样特征即解理断裂，同时也呈现出了一定的微孔洞特征，即有韧性断裂的特点，如图 8(a)所示，属韧脆性混合断裂；对于缺口试件，不同缺口程度均表现出较明显的微孔洞断裂的特征，在图 8(b)中能清晰地看到韧窝聚合、连接的特点。这些特征与试件在宏观破坏形式上的表现是一致的，即光滑圆柱试件破坏是由混合损伤机制引起的，而缺口试件破坏则是由微孔洞损伤演化机制决定的。J-C失效模型在微观上反映的是材料的微孔洞损伤演化机理，在宏观上体现为该微观损伤机理导致的材料断裂延性变化，不能体现其他变形机制的作用，这就是模拟结果可以描述光滑圆柱试件的杯锥形破坏特点而无法描述其整体剪切特征的原因。
4. 结论
(1) 通过缺口圆柱试件设计能够实现镁合金MB2不同程度的多向应力状态，结合SHTB装置可以实现其在复杂应力状态下的动态拉伸加载研究。
(2) 在研究的实验条件范围内，应力状态对镁合金MB2破坏行为的影响存在明显的转折点，而应变率(5 000 s-1以内)则不存在转折点。通过模型修正和参数拟合得到了镁合金MB2的等效破坏应变准则，且其数值模拟结果可以较好地体现拉伸试件的杯锥形破坏特征。
(3) 镁合金MB2不同应力状态下的破坏行为与其微观损伤机理密切相关，随着应力三轴度的增加，其微观损伤机制由混合断裂转变为韧窝断裂，这是导致其宏观延性和破坏模式发生变化的重要原因。
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图 3 退火态SLM AlSi10Mg合金xOy面和xOz面微观组织图像
Figure 3. Microstructure of xOy plane and xOz plane of SLM AlSi10Mg alloy after annealing treatment
图 5 室温及173 K、不同应变率下的真实应力-应变曲线
Figure 5. True stress-strain curves under different strain rates at room temperature and 173 K
图 6 室温下ɛ=0.1时不同应变率与流动应力的关系
Figure 6. Relationship between different strain and flow stress at room temperature when ɛ=0.1
图 7 0.002 s−1不同温度下的真实应力-应变曲线和温度与流动应力的关系
Figure 7. True stress-strain curves at different temperatures under 0.002 s−1 and relationship between temperature and flow stress
图 9 J-C本构模型计算数据与实验数据
Figure 9. Comparison between experimental and calculated data from J-C constitutive model
图 11 J-C本构模型计算数据与实验数据
Figure 11. Comparison between experimental data and calculated data from J-C constitutive model
图 12 本构模型预测值与实验值的相关性
Figure 12. Correlation between experimental and predicted stress from constitutive model
图 13 室温及高温下本构模型的验证
Figure 13. Verification of constitutive models at room temperature and high temperature
表 1 AlSi10Mg粉末组分的质量分数
Table 1. Mass fraction of AlSi10Mg powder
% Al Si Mg Fe Mn Cu Ti 88.93 10.32 0.29 0.16 0.10 0.05 0.15 
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表 2 AlSi10Mg打印工艺参数
Table 2. Processing parameters of AlSi10Mg
激光功率/
W扫描速度/
(m·s−1)扫描间距/
mm层厚/
mm旋转角度/
(°)预热温度/
K300 1.2 0.2 0.03 30 423
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表 3 修正后的J-C本构模型参数
Table 3. Modified J-C constitutive model parameters
A/MPa B/MPa n C1 C2 k 223 120 0.33 0.014 1.83×10−5 2.71
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表 4 修正后的J-C本构模型温度参数
Table 4. Modified J-C constitutive model of temperature parameters
T/K m 373 1.026 473 0.879 573 0.590
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表 5 低温J-C本构模型参数
Table 5. J-C constitutive model parameters at low temperature
A/MPa B/MPa n C m 234.08 145.02 0.3 0.014 2.91
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