复合材料层合结构极限强度预测方法及分层应力最小化研究
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摘要
纤维增强复合材料(FRP)是由高强度、低密度的纤维材料与基体组成，具有很多其它材料和结构不具有的优点或特点，如比强度和比模量很高，具有强烈的各向异性和可设计性等，广泛应用于航空、航天、造船和汽车等领域。纤维金属混杂层合板(FML)是最近几年出现的一种新型复合材料结构。FML由纤维增强树脂层与金属薄板层交替粘接而成。FML具有抗冲击性能好；防火、防腐蚀性能好；抗疲劳性能好等优点。因此FML是一种很有应用前景的航空航天材料。为了保证FRP层合板或FML混杂层合板结构在航空航天领域的安全应用，其强度特征和强度预测方法的研究显得尤为重要。复合材料层合板有多种不同的失效模式，分层失效是层合结构所独有的一种失效模式，对易于分层的铺层结构，忽略分层失效会使预测的失效强度远高于实际值。因此在对复合材料层合结构的极限强度进行预测时，必须考虑分层失效的影响，并且有必要采用优化技术最大程度的降低分层失效发生的可能性。针对以上问题，本文的主要研究内容和取得的成果如下：
(1)提出了复合材料层合板强度预测的数值模型。采用有限元方法对复合材料层合板进行结构分析，根据Tsai-Wu准则来判断层合板的面内失效，利用APDL编制程序来模拟层合板在加载过程中的逐步失效过程，得到了层合板的极限强度。在此基础上，将实验和有限元分析法相结合来评价层合板的强度，系统研究了准各向同性层合板的极限强度与加载方向(层合结构)之间的关系，对损伤规律以及强度特征进行了预测和讨论。在一定范围内揭示了不同的准各向同性板的内部损伤扩展规律和强度特征，为层合板结构的强度预测，以及复合材料的优化设计提供依据和参考。
(2)对上述仅考虑面内失效的逐步失效模型进行了改进，建立了同时考虑面内失效和源于自由边界处层间应力的分层失效的强度预测模型和方法。采用改进的数值模型计算得到了多组层合板的分层起始强度以及最终失效强度，计算结果和文献中的实验结果相当符合。相比仅考虑面内失效的逐步失效模型和方法可以更全面的预测层合板的逐步失效过程。这对复合材料失效机理认识的深化，和更加安全可靠地利用复合材料层合结构有着重要的意义。
(3)针对分层失效由层间正应力主导的特点，构筑了自由边界处层间正应力的最小化问题，建立了相应的模型和数值求解方法。对于实际工程中的高度非线性、多局部极值、目标函数不可导等复杂问题，传统的梯度型优化算法常常存在函数求导困难或不能求导的问题，导致优化问题无法进行。为此，本文首先采用ANSYS自带的零阶优化方法进行求解。该方法只需用到目标函数或约束函数的值，而不需要用到它们的导数。优化结果显示出了一定的精度，然而优化结果具有初值敏感性。为此，本文提出了将智能进化算法PSO和FEM相结合的思想，开发了通用有限元软件和粒子群优化算法之间的接口程序。构造了三类基于层间正应力的目标函数，对层合板的铺层进行了优化。通过与零阶优化方法的比较，论证了提出的优化方法用于复杂工程优化设计问题的可行性和优越性。
(4)针对新型纤维金属混杂层合板(FML)结构，将传统的经典层合板理论进行了修改和扩充使之适用于FML。分别采用修改的层合板理论和基于ANSYS的数值方法对FML进行了拉伸试验模拟，得到的应力应变曲线与已有文献试验结果相符。采用ANSYS计算层合板在不同荷载下的应力响应，并结合失效准则得到失效因子。以失效因子最大和最小为目标，分别对FML和FRP中的纤维铺层角度进行了优化。基于得到的优化结果对FRP和FML的强度性能进行了比较。结果表明：由于金属层的加入，使得FML相比FRP具备更好的抵抗双向拉伸载荷及面外集中载荷(低速冲击载荷)作用的能力。
By virtue of its excellent properties, such as the high specific strength and high specific modulus, anisotropy and designability, the Fiber Reinforced Plastics (FRP) has been widely used as structure materials in aircraft, space, marine and automobile, etc. Fiber metal hybrid laminate (FML) is a new class of composite material structure arisen in recent years. It consists of thin aluminum alloy sheets bonded together with fiber-reinforced epoxy prepreg. These laminates exhibit favourable characteristics, such as excellent impact properties, fire and corrosion behavior and fatigue properties. These advantages further facilitate the use of FML for primary structures in aerospace industry. In order to guarantee secure use of FRP or FML in aeronautical applications, their strength characteristic and evaluation is of great concern. For a loaded laminate, there are several failure modes among which delamination is a primary failure mode unique to composite laminates. For laminates prone to delaminating, the predicted ultimate failure strength will be overestimated if delamination is neglected. Thus, it is crucial to take the delamination into account when predicting the ultimate failure strength of laminated composites, and it is essential to minimize delamination tendency by optimization technology.
Aiming at the problems mentioned above, the main contents and achievements in this paper are listed as follows:
(1) A numerical method for predicting ultimate strength of composite laminates is proposed. The proposed method adopts FEM to conduct structural analysis and Tsai-Wu criterion is utilized to account in-plane failure of laminates. The progressive failure process is modeled through APDL incorporated in ANSYS and the ultimate failure strength of laminates is obtained. The failure characteristics of CF/EP quasi-isotropic laminates are discussed and the effect of loading direction and stacking sequence on the ultimate strength is investigated through experiments and numerical analyses.
(2) The proposed method above considering only in-plane failure is improved by accounting delamination failure attributed to the interlaminar stresses at the free-edge additionally. The improved method is used to predict the onset strength of delamination and the ultimate strength of various lay-ups. The predicted results show excellent agreement with the experimental results available in literature. Thus, in comparison to the method considering only in-plane failure, the improved method can lead to a more comprehensive failure process. It is of great significance in further understanding the failure mechanism and exploiting laminated composites more safely and reliably.
(3) Considering that delamination failure is mainly attributed to interlaminar normal stresses, an objective function is presented to minimize the interlaminar normal stresses at the free-edge. In practical engineering problems, optimization may deal with functions which are discontinuous or un-differentiable, highly nonlinear, or multiple local extreme. It makes the optimization problems difficult or even impossible to be solved by traditional methods which require at least the first derivative of the objective function with respect to the design variables. In view of this, the zero-order method (ZOM) incorporated in ANSYS which requires only the value of the objective function and the constraint functions is firstly adopted for optimization. ZOM can yield a satisfactory optimal solution. However, the solutions of ZOM exhibit sensitivity to the initial designs. In order to overcome this disadvantage, a technique of applying an evolution-based optimization algorithm PSO integrated with the general FE code ANSYS is developed for optimization. Examples dealing with the optimization of three different functions of interlaminar normal stresses are presented to demonstrate the feasibility and superiority of the proposed approach.
(4) Aiming at the new class of composite structure FML, traditional CLT is modified and extended to nonlinear cases. Modified CLT and FEM are utilized to simulate the stress-strain behavior of FML under tensile loading. The simulated stress-strain curves agree well with the experimental results available in literature. Subsequently, ANSYS is utilized to perform the structural analysis of laminates under different loads, and the failure indices are obtained through failure criterions. The maximum and minimum failure index of FRP and FML have been found out respectively via altering the fiber orientations of prepreg layers. Based upon the optimization results, the strength behavior of FML and FRP are compared. The optimization results demonstrate that owing to the substituting of metal alloy sheet for prepreg layer, FML is of better capability to withstanding biaxial load and out of plane concentrating load (low-velocity impact load) than FRP.
(1)提出了复合材料层合板强度预测的数值模型。采用有限元方法对复合材料层合板进行结构分析，根据Tsai-Wu准则来判断层合板的面内失效，利用APDL编制程序来模拟层合板在加载过程中的逐步失效过程，得到了层合板的极限强度。在此基础上，将实验和有限元分析法相结合来评价层合板的强度，系统研究了准各向同性层合板的极限强度与加载方向(层合结构)之间的关系，对损伤规律以及强度特征进行了预测和讨论。在一定范围内揭示了不同的准各向同性板的内部损伤扩展规律和强度特征，为层合板结构的强度预测，以及复合材料的优化设计提供依据和参考。
(2)对上述仅考虑面内失效的逐步失效模型进行了改进，建立了同时考虑面内失效和源于自由边界处层间应力的分层失效的强度预测模型和方法。采用改进的数值模型计算得到了多组层合板的分层起始强度以及最终失效强度，计算结果和文献中的实验结果相当符合。相比仅考虑面内失效的逐步失效模型和方法可以更全面的预测层合板的逐步失效过程。这对复合材料失效机理认识的深化，和更加安全可靠地利用复合材料层合结构有着重要的意义。
(3)针对分层失效由层间正应力主导的特点，构筑了自由边界处层间正应力的最小化问题，建立了相应的模型和数值求解方法。对于实际工程中的高度非线性、多局部极值、目标函数不可导等复杂问题，传统的梯度型优化算法常常存在函数求导困难或不能求导的问题，导致优化问题无法进行。为此，本文首先采用ANSYS自带的零阶优化方法进行求解。该方法只需用到目标函数或约束函数的值，而不需要用到它们的导数。优化结果显示出了一定的精度，然而优化结果具有初值敏感性。为此，本文提出了将智能进化算法PSO和FEM相结合的思想，开发了通用有限元软件和粒子群优化算法之间的接口程序。构造了三类基于层间正应力的目标函数，对层合板的铺层进行了优化。通过与零阶优化方法的比较，论证了提出的优化方法用于复杂工程优化设计问题的可行性和优越性。
(4)针对新型纤维金属混杂层合板(FML)结构，将传统的经典层合板理论进行了修改和扩充使之适用于FML。分别采用修改的层合板理论和基于ANSYS的数值方法对FML进行了拉伸试验模拟，得到的应力应变曲线与已有文献试验结果相符。采用ANSYS计算层合板在不同荷载下的应力响应，并结合失效准则得到失效因子。以失效因子最大和最小为目标，分别对FML和FRP中的纤维铺层角度进行了优化。基于得到的优化结果对FRP和FML的强度性能进行了比较。结果表明：由于金属层的加入，使得FML相比FRP具备更好的抵抗双向拉伸载荷及面外集中载荷(低速冲击载荷)作用的能力。
By virtue of its excellent properties, such as the high specific strength and high specific modulus, anisotropy and designability, the Fiber Reinforced Plastics (FRP) has been widely used as structure materials in aircraft, space, marine and automobile, etc. Fiber metal hybrid laminate (FML) is a new class of composite material structure arisen in recent years. It consists of thin aluminum alloy sheets bonded together with fiber-reinforced epoxy prepreg. These laminates exhibit favourable characteristics, such as excellent impact properties, fire and corrosion behavior and fatigue properties. These advantages further facilitate the use of FML for primary structures in aerospace industry. In order to guarantee secure use of FRP or FML in aeronautical applications, their strength characteristic and evaluation is of great concern. For a loaded laminate, there are several failure modes among which delamination is a primary failure mode unique to composite laminates. For laminates prone to delaminating, the predicted ultimate failure strength will be overestimated if delamination is neglected. Thus, it is crucial to take the delamination into account when predicting the ultimate failure strength of laminated composites, and it is essential to minimize delamination tendency by optimization technology.
Aiming at the problems mentioned above, the main contents and achievements in this paper are listed as follows:
(1) A numerical method for predicting ultimate strength of composite laminates is proposed. The proposed method adopts FEM to conduct structural analysis and Tsai-Wu criterion is utilized to account in-plane failure of laminates. The progressive failure process is modeled through APDL incorporated in ANSYS and the ultimate failure strength of laminates is obtained. The failure characteristics of CF/EP quasi-isotropic laminates are discussed and the effect of loading direction and stacking sequence on the ultimate strength is investigated through experiments and numerical analyses.
(2) The proposed method above considering only in-plane failure is improved by accounting delamination failure attributed to the interlaminar stresses at the free-edge additionally. The improved method is used to predict the onset strength of delamination and the ultimate strength of various lay-ups. The predicted results show excellent agreement with the experimental results available in literature. Thus, in comparison to the method considering only in-plane failure, the improved method can lead to a more comprehensive failure process. It is of great significance in further understanding the failure mechanism and exploiting laminated composites more safely and reliably.
(3) Considering that delamination failure is mainly attributed to interlaminar normal stresses, an objective function is presented to minimize the interlaminar normal stresses at the free-edge. In practical engineering problems, optimization may deal with functions which are discontinuous or un-differentiable, highly nonlinear, or multiple local extreme. It makes the optimization problems difficult or even impossible to be solved by traditional methods which require at least the first derivative of the objective function with respect to the design variables. In view of this, the zero-order method (ZOM) incorporated in ANSYS which requires only the value of the objective function and the constraint functions is firstly adopted for optimization. ZOM can yield a satisfactory optimal solution. However, the solutions of ZOM exhibit sensitivity to the initial designs. In order to overcome this disadvantage, a technique of applying an evolution-based optimization algorithm PSO integrated with the general FE code ANSYS is developed for optimization. Examples dealing with the optimization of three different functions of interlaminar normal stresses are presented to demonstrate the feasibility and superiority of the proposed approach.
(4) Aiming at the new class of composite structure FML, traditional CLT is modified and extended to nonlinear cases. Modified CLT and FEM are utilized to simulate the stress-strain behavior of FML under tensile loading. The simulated stress-strain curves agree well with the experimental results available in literature. Subsequently, ANSYS is utilized to perform the structural analysis of laminates under different loads, and the failure indices are obtained through failure criterions. The maximum and minimum failure index of FRP and FML have been found out respectively via altering the fiber orientations of prepreg layers. Based upon the optimization results, the strength behavior of FML and FRP are compared. The optimization results demonstrate that owing to the substituting of metal alloy sheet for prepreg layer, FML is of better capability to withstanding biaxial load and out of plane concentrating load (low-velocity impact load) than FRP.
引文
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