Performance deterioration behavior of photovoltaic cells subjected to massive-particles impact environment
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摘要: 光伏电池由于具有较高的光电转化效率，在沙漠等太阳能充足的地方被广泛应用。但在沙尘长期冲击的环境下，光伏电池内部结构易出现累积损伤，使光电转化效率大幅降低。因此，研究颗粒群冲击条件下光伏电池的力-电行为具有重要意义。基于分离式霍普金森压杆，发展了一种驱动较大尺寸颗粒群高速冲击的实验方法，并系统测量了不同冲击条件下，多晶硅光伏电池的损伤行为与光电转化性能衰减规律。研究结果表明，随着颗粒直径、冲击速度和数密度的增加，光伏电池的光电转换效率快速降低；颗粒冲击后光伏电池表现出三种典型的损伤模式，并给出了对应的应力阈值条件。基于实验测试结果，发展了多晶硅光伏电池颗粒群冲击损伤诱导光电转化性能退化模型，为沙砾冲击环境下光伏电池光电性能衰减规律提供了有效的预测方法。Abstract: Photovoltaic cells have been widely used in desert areas and other solar-rich environments due to the relatively high solar energy to electricity conversion efficiency. Under the long-term dust impact condition in the desert dust environment, the internal structures of photovoltaic cells are prone to damage, resulting in a significant deterioration of photoelectric conversion efficiency. Therefore, it is of great significance to understand the photoelectric response of photovoltaic cells subjected to massive particles impact. Firstly, a millimeter-scale high-speed particle impact experimental method was developed based on split Hopkinson pressure bar (SHPB) facility. The experimental results showed that the damage of the photovoltaic cell was mainly caused by the first impact, leading to the damage characteristics including shear microcracking, brittle fracture and delamination. Then, the critical stresses corresponding to the three failure modes were analyzed in terms of the initial impact kinetic energy. The first failure mode assumes that high-speed particles behave as fluids, so impulsive compressive stresses are used in the model. The damage in the second failure mode comes from high contact stresses on the impacted surface. The damage in the third mode of failure comes from bending stresses. The photovoltaic performance degradation of the photovoltaic cells after impact under different particle velocities, diameters, and number densities were investigated, showing that the photoelectric conversion efficiency of the photovoltaic cells decreased significantly with the increase of the particle size, the impact velocity, and the number density. Finally, a damage-induced photovoltaic performance degradation (DPPD) model under sand and gravel impact conditions is established to quantitatively describe the influence of impact parameters on the photovoltaic conversion efficiency, in which the two-dimensional damage factor D is proposed to represent the average damage level of the damaged area. The results of the DPPD model are in agreement with the experimental results, validating the applicability of the model for predicting accurately the photovoltaic cell photovoltaic performance under massive sand and gravel impact environment.
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金属铍具有中子散射截面大、吸收截面小、硬度高、模量高、比强高、热学性能良好等特性，因此被广泛应用于航空航天、军事工业、医疗设备、焊接技术等多个技术领域，如中子反射层，反应堆第一壁材料、中子慢化剂，航空航天结构部件、精密仪表、光学器件及X射线管窗口等。国外已开展大量金属铍的变形行为研究，而国内开展的相关研究较少，且主要集中在常温静态拉伸性能方面，对其压缩力学行为尤其是动态压缩特性方面报道较少[1-9]。王零森等[1]研究了晶粒尺寸对铍静态拉伸力学性能的影响，发现随着晶粒度逐渐细化，铍材料的强度显著提高，而晶粒过粗或过细，延伸率均下降。许德美等[2-3]研究了组织缺陷对金属铍室温拉伸断裂行为的影响，其分析结果表明铍的“脆性”特征主要来源于杂质、片状晶体疏松和孔洞等初始缺陷，最关键因素是杂质的尺寸、间距和其在材料内部的分布形态。W.R.Blumenthal等[4-5]对不同制备工艺下的铍进行了较为系统的研究。实验结果表明，铍的压缩应力应变响应具有较强的应变率敏感性和一定的热软化效应，并指出孪生是高应变率下铍变形的主要机制。D.W.Brown等[6-8]系统开展了应变率对热压和轧制铍的力学性能和变形机理的研究工作，分析结果表明屈服强度对应变率不敏感，而加工硬化则受织构的影响具有较强的率相关性。T.Nicholas[9]和D.Breithaupt[10]研究了铍在常温102~103 s-1应变率下的动态压缩性能，结果表明铍具有良好的塑性，应变增大至0.25时样品才发生断裂。由此可见，国外开展的相关研究工作重点关注制备工艺、温度、应变率等条件对金属铍滑移及孪晶变形机制的影响研究，获得描述金属铍变形织构行为的本构模型参数。国内开展的研究则主要围绕金属铍静态拉伸应力状态下的“脆性”行为的微观变形机制，对其压缩行为研究工作较少，尤其是动态加载下温度、应变速率对其变形行为的影响未见相关研究报道。
本文中利用材料实验机及Hopkinson杆装置系统开展了热等静压金属铍在不同温度、应变率下的压缩力学行为研究，获得金属铍压缩载荷下强度、塑性与实验温度、应变率之间的对应关系。并采用Johnson-Cook本构模型对获得的应力应变曲线进行拟合，模型计算结果与实验结果吻合较好。
1. 实验材料及方法
铍在机加后表面会有较大的残余应力，为了消除残余应力对测量结果的影响[11]，室温力学实验前对样品进行了蚀刻处理，蚀刻剂配方为：H3PO4，750 mL；H2SO4，30 mL；Cr2O3，71 mg；H2O，200 mL。蚀刻方法为将铍试样放入酸洗液约50 s取出，用蒸馏水等清洗干净。
静态力学实验在CMT5105型材料试验机及其配置的高温真空炉中进行，高温炉温度控制精度为±3 ℃，真空度优于1×10-2 Pa，试样在1 h内加热到规定温度，保温15 min后开始实验，应变率为1.0×10-3 s-1，测试温度范围为室温至800 ℃。动态压缩实验采用∅10 mm的Hopkinson杆装置。试样为∅5 mm×5 mm的圆柱体，应变率范围为0.5×103~2.5×103 s-1, 在常温下进行。
2. 实验结果与分析
图 1所示为铍在不同温度下的准静态压缩实验结果。由图 1应力应变曲线可以看出，金属铍在室温至800 ℃的温度范围内压缩变形具有良好的塑性。屈服强度和流动应力随实验温度升高而降低，加工硬化行为也随之降低。图 2所示为不同固定应变下的流动应力随实验温度的变化。由图中可以看到，在室温至200 ℃时，不同固定应变下流动应力均下降较快，高于200 ℃时流动应力下降趋势变缓，呈线性下降特征。当实验温度高于400 ℃时，不同应变下的流动应力值基本一致，这表明此时材料的塑性变形行为趋于理性塑性流动。
图 1 金属铍在准静态条件下应力应变关系Figure 1. Relation between stress and strain under quasi-static condition
图 2 金属铍在准静态条件下流动应力随温度变化曲线Figure 2. Relation between flow stress and temprature under quasi-static condition图 3所示为铍的动态压缩实验结果。可以看出，铍的屈服强度和加工硬化行为随应变率增大而显著增大，在初始变形阶段，加工硬化行为呈现非线性特征，随变形量增大，转变为线性硬化。由文献[4]可知，准静态和动态加载下，金属铍的塑性变形控制机制有显著区别。与大多数对称性低、滑移系统少的密排六方晶系金属一样，由于晶体的取向不利于发生滑移，孪生成为铍塑性变形的重要方式。在初始变形阶段，变形机制由位错滑移控制，随着变形增大，位错滑移困难，通过孪生协调变形，尤其在动态加载过程中，晶粒内部将产生大量的孪晶，由于滑移与孪生机制的竞争导致了不同应变率、不同应变下金属铍屈服强度和加工硬化行为的显著区别。
3. 本构模型
Johnson-Cook模型是目前应用最广泛的本构模型之一，模型中将流动应力表述为应变硬化效应、应变率效应和温度软化效应的乘积，方程的基本形式如下：
σ=(A+Bεnp)(1+Cln˙ε˙ε0)(1−T∗m) (1) 式中:σ为Von-Mises流动应力，εp为等效塑性应变，A为准静态下的屈服应力，B为应变硬化系数，n为应变硬化指数，˙ε0为参考应变率(可取准静态应变率)，C为应变率敏感系数，T*为温度相关项，具体表达式为(T-Tr)/(Tm-Tr), Tr和Tm分别为参考温度和熔化温度，一般取Tr为300 K，m为热软化系数。由式(1)可见，Johnson-Cook本构模型忽略了材料变形历史的影响，即如果材料服从Johnson-Cook本构模型，则不同应变率下的应力应变曲线是相似的。
而由图 1~3中的应力应变曲线可以看到，不同温度或应变率下铍的应力应变曲线呈发散趋势，传统的Johnson-Cook本构模型已不适用。因此，本文中采用一个修正的Johnson-Cook本构模型对实验数据进行拟合，在应变硬化项中增加屈服强度温度相关线性函数，同时参考Zerrilli-Armstrong本构模型中描述hcp晶体结构材料变形硬化的函数关系式, 在幂指数应变硬化项中添加应变率指数硬化项和温度指数软化项，分别描述温度、变形历史对材料屈服强度和流动应力的影响，以及流动应力随应变率明显的增加趋势, 其表达式为：
σ=[A(1−A1T∗)+Bεnpea˙ε(B1+B2eβT∗)](1+Cln˙ε˙ε0) (2) 和传统Johnson-Cook模型相比，修正模型中增加了4个参数。取准静态应变率10-3 s-1为参考应变率，Tm=1 557 K。本构拟合参数为：A=424 MPa, B=1 010 MPa, A1=1.487, B1=0.107 3, B2=0.885 4, n=0.485, α=0.000 39, β=-13.83, C=0.015。
采用修正模型计算结果与实验结果对比如图 4所示，实线为采用修正Johnson-Cook本构模型的计算结果。可以看到，模型的计算结果与实验结果符合较好，修正后的Johnson-Cook本构模型能够较好地描述金属铍在不同温度、应变和应变率下的压缩变形行为。
图 4 修正Johnson-Cook模型计算结果与实验结果对比Figure 4. Comparison of experimental results with calculated results by modified Johnson-Cook model4. 结论
本文中研究了较宽温度范围和应变率下热等静压金属铍的压缩力学行为。结果表明铍的屈服强度和加工硬化行为随应变率的提高而显著增大，随温度的升高而降低。常温下其加工硬化行为在初始变形阶段呈现非线性特征，随变形增大转变为线性硬化。温度高于400 ℃时，其变形行为趋于理性塑性流动。考虑温度、变形历史对材料屈服强度和加工硬化的影响，对Johnson-Cook模型进行了修正，修正后的本构模型预测结果和实验结果吻合较好。
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图 2 颗粒群冲击实验示意图
Figure 2. Schematic diagram of massive-particles impacting photovoltaic cells
图 3 颗粒冲击光伏电池过程（颗粒数N=15，冲击速度v=65 m/s，粒径d=3 mm）
Figure 3. Impact history of particles on the photovoltaic cell (N=15, v=65 m/s, d=3 mm)
图 6 光伏电池受冲击前后的典型电输出曲线
Figure 6. Typical electrical output curves of photovoltaic cells before and after impact by massive particles
图 7 光电转化效率衰减与小颗粒冲击速度关系（实验数据、DPPD模型拟合结果）
Figure 7. Photovoltaic cell damage characterization versus particle impact velocity (experimental data and DPPD model fitting results)
表 1 光伏电池冲击前后光电测试结果
Table 1. Light-electricity conversion performance of the photovoltaic cells before and after impact
测试编号 颗粒直径/mm 冲击速度m/s 颗粒数 输出功率变化/% 光电转化效率/% 损伤特征 1 3 0 0 0 19.0 完好 2 3 30 5 0 19.0 完好 3 3 40 5 −0.8 18.8 微裂纹 4 3 45 5 −3.2 18.4 微裂纹 5 3 55 5 −6.1 17.8 明显断裂 6 3 45 1 −0.8 18.8 微裂纹 7 3 55 1 −1.4 18.7 明显断裂 8 3 65 1 −2.2 18.6 分层脱胶 9 3 65 10 −22.2 14.7 分层脱胶 10 3 65 15 −30.0 13.3 分层脱胶 11 2 65 10 −0.1 19.0 微裂纹 12 2 87 10 −9.9 17.2 明显断裂 13 2 122 10 −27.0 13.9 分层脱胶 14 2 84 15 −12.3 16.7 明显断裂 15 2 128 15 −36.0 12.3 分层脱胶 16 1 128 100 −2.3 19.0 完好 17 3 45 5 −12.5 16.6 明显断裂 2 87 10 18 3 65 10 −23.0 14.6 分层脱胶 2 
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