CAJ | 학술논문

本文采用弹性理论,研究了鼓泡法试验过程中,外力(P)与薄膜中心挠度(w_0)之间的本构关系,计算出P与w_0的数学表达式.该分析模型考虑了薄膜内延展变形及薄膜中残余拉应力对本构关系的影响,并在较大挠曲区间范围内(挠度为10~(-2)～10~2倍薄膜厚度)分析本构关系特征.分析结果表明,外力与薄膜中心挠度之间本构关系可表示为:P∝w_0~n,n为指数.随着薄膜中心挠度的增加,薄膜的主要力学行为由弯曲过渡到延展,本构关系由线性过渡到立方关系,本构关系方程指数n由1增加到3.利用本构方程进行数值计算结果表明,薄膜挠曲所需外力随着薄膜半径增加而减小,随着残余拉应力的增加而增加.相对于以往不考虑延展变形的小挠度模型,本文所提出的力学模型更适合于大挠度条件下鼓泡法试验.
본문채용탄성이론,연구료고포법시험과정중,외력(P)여박막중심뇨도(w_0)지간적본구관계,계산출P여w_0적수학표체식.해분석모형고필료박막내연전변형급박막중잔여랍응력대본구관계적영향,병재교대뇨곡구간범위내(뇨도위10~(-2)～10~2배박막후도)분석본구관계특정.분석결과표명,외력여박막중심뇨도지간본구관계가표시위:P∝w_0~n,n위지수.수착박막중심뇨도적증가,박막적주요역학행위유만곡과도도연전,본구관계유선성과도도립방관계,본구관계방정지수n유1증가도3.이용본구방정진행수치계산결과표명,박막뇨곡소수외력수착박막반경증가이감소,수착잔여랍응력적증가이증가.상대우이왕불고필연전변형적소뇨도모형,본문소제출적역학모형경괄합우대뇨도조건하고포법시험.
The constitutive relation between external force (P) and central deflection (w_0) of thin film in blister test was studied by elasticity theory. The close form solutions on the external force and deflection were obtained for studying the constitutive relation in a range of w_0=(10~(-2)·10~2) h, with h being the thickness of thin film. The stretching behavior of thin film and residual tensile stress were included into the analytical model. The results show that the constitutive relation is expressed as the form of P∝w_0, with n being the power. With respect to the deflection of thin film increasing, the dominant behavior of thin film changes from bending to stretching, and the constitutive relation changes from linear (n = 1) to cubic (n=3). The analysis also shows that the external force needed to deflection thin film decreases with respect to the radius of thin film increasing, but increases with respect to the residual tensile stress increasing. Compared to those small deflection plate models that ignore the stretching of thin film, the present model is more suitable for the cases that the deflection of thin film in the blister is larger compared to the thickness of thin film.