图  1  含离散损伤模型的求解区域Ω₀

Figure  1.  A solve domain Ω₀ with discrete damage zone model

$\bar t $—Load; $\bar u $—Displacement ; $\varGamma_{\rm{t}} $—Load boundary ; $\varGamma_{\rm{tf}} $—Surface force region; $ \varGamma_{\rm{c}}$—Damage region; $\varGamma_{\rm{coh}} $—Cohesion region; $\varGamma_{\rm{u}} $—Displacement boundary

图  2  离散损伤模型的损伤演化关系

Figure  2.  Pure mode damage evolution law for discrete damage zone model

(${\delta ^{{\rm{cr}}}},\;F^{{\rm{cr}}} $)—Critical point; $K_0 $—Initial stiffness; $(1-D_{{\rm{n}}})K_0 $—Damage stiffness; $K_{\rm{p}} $—Penalty stiffness

图  3  疲劳加载的载荷大小变化

Figure  3.  Variation of the applied moment with increment during fatigue loading

图  4  离散损伤模型的疲劳本构关系

Figure  4.  Fatigue damage evolution law for discrete damage zone model

1—Began to damage; 2—Damage; 2’—Failure; $F_0 $—Spring load; $\delta_0 $—Critical displacement; $\delta_{\rm{c}} $—Maximum displacement

图  5  疲劳渐进扩展逐层方法的位移场

Figure  5.  Displacement field for fatigue progressive extended layerwise method

h_k—Thickness of layer k; z_k—Coordinate in thickness direction of layering interfaces of layers k and (k−1); The numbers on the left represent the mathematical layer interpolation nodes of the displacement field along the thickness direction, and the numbers on the right represent the interfaces between the layers

图  6  HTC/6736A碳纤维双悬臂梁(DCB)模型和加载方式

Figure  6.  HTC/6736A carbon fiber double cantilever beam (DCB) model and load model

L—Length; B—Width; 2h—Thickness; a₀—Initial delamination length; M—Moment

图  7  HTC/6736A双悬臂梁分层长度-载荷循环次数曲线

Figure  7.  HTC/6736A double cantilever beam model delamination length versus loading cycles

图  8  疲劳渐进扩展逐层方法(FPXLWM)模拟得到HTC/6736A碳纤维双悬臂梁的Paris曲线

Figure  8.  Paris plot of HTC/6736A carbon fiber double cantilever beam calculated by fatigue progressive extended layerwise method (FPXLWM)

图  9  不同C值计算得到HTC/6736A双悬臂梁的Paris曲线(β=2.0、λ=0.5)

Figure  9.  Multiple groups of paris plots of HTC/6736A double cantilever beams with different values of C (β=2.0, λ=0.5)

图  10  不同β值计算得到HTC/6736A碳纤维双悬臂梁的Paris曲线(C=1.0、λ=0.5)

Figure  10.  Multiple groups of paris plots of HTC/6736A carbon fiber double cantilever beams with different values of β (C=1.0, λ=0.5)

图  11  不同λ值计算得到HTC/6736A碳纤维双悬臂梁的Paris曲线(C=1.0、β=2.0)

Figure  11.  Multiple groups of paris plots of HTC/6736A carbon fiber double cantilever beams with different values of λ (C=1.0, β=2.0)

图  12  实验数据匹配得到HTC/6736A碳纤维双悬臂梁的Paris曲线

Figure  12.  Paris plots of HTC/6736A carbon fiber carbon fiber double cantilever beam with experimental and FPXLWM

图  13  不同加速倍数ΔN计算得到HTC/6736A碳纤维双悬臂梁的a-N曲线(循环载荷30 N、网格尺寸l_s=0.25 mm)

Figure  13.  Delamination growths of HTC/6736A carbon fiber double cantilever beams with loading cycles for different computing speed ΔN (Applied load is 30 N, mesh scale l_s=0.25 mm)

图  14  HTC/6736A碳纤维双悬臂梁不同网格尺寸l_s对应疲劳参数C的值(循环载荷30 N、加速倍数ΔN=200)

Figure  14.  Variation of fatigue parameter C with different values of mesh scale l_s of HTC/6736A carbon fiber double cantilever beam (Applied load is 30 N, computing speed ΔN=200)

图  15  不同网格尺寸计算得到HTC/6736A碳纤维双悬臂梁的a-N曲线

Figure  15.  Delamination growths of HTC/6736A carbon fiber double cantilever beams with loading cycles for different mesh scale l_s

图  16  铺层顺序为[0]₄的HTC/6736A碳纤维双悬臂梁宽度方向三个位置的a-N曲线(循环载荷20 N、网格尺寸l_s=0.25)

Figure  16.  Delamination length of HTC/6736A carbon fiber double cantilever beam at three positions in width direction for stacking sequence [0]₄ (Applied load is 20 N, mesh scale l_s=0.25)

图  17  不同铺层顺序HTC/6736A碳纤维双悬臂梁宽度方向上两个位置的a-N曲线(循环载荷20 N)

Figure  17.  Delamination length of HTC/6736A carbon fiber double cantilever beam with loading cycles at two positions in width direction with different stacking sequences (Applied load is 20 N)

图  18  不同铺层顺序HTC/6736A碳纤维双悬臂梁载荷-寿命曲线

Figure  18.  S-N curves of HTC/6736A carbon fiber double cantilever beam specimens with different stacking sequences