現今對於材料界面的混合模式破壞韌性與混合模式疲勞裂紋成長的資料缺乏、分析與預測少，專門量測此特性的儀器更少，本論文的主要目的為發展一套量測材料受混合模式指定任意相位角作用下的破壞韌性或疲勞裂紋成長特性的儀器。此拉伸試驗機台除了界面混合模式疲勞破壞實驗外，亦可以量測破壞韌性、潛變、應力鬆弛、等機械性值。本論文著重於界面疲勞破壞實驗，內容包含混合模式相位角在零度、負三十度、負四十五度的界面疲勞脫層實驗之建立及得到此界面脫層之疲勞特性常數，進而推演至材料受任意指定相位角。
本論文所發展之量測系統透過兩個音圈馬達對雙懸臂樑試件施加不相等之作用力以構成混和模式彎矩，應用彈性基底之雙懸臂樑理論，藉此從實驗量測所得之雙懸臂樑開口量與作用力關係計算每一疲勞周次的裂紋長度及應變能釋放率，再藉由控制程式回饋計算下一周次施力大小，以確保相位角不變。分析鋁-環氧樹脂界面疲勞裂紋成長特性發現在零度、負三十度與負四十五度相位角下的界面疲勞特性冪次率指數常數分別為1.58、0.945與0.685。

Development of a characterization system for interface delamination fatigue growth under mixed-moded loading
Sian-Jyun, Kuo
Tz-Cheng, Chiu
Mechanical Engineering, National Cheng Kung University
SUMMARY
In this research an experimental characterization system for interface delamination crack growth under fatigue mixed-moded bending is developed. The mixed mode loading is achieved by applying prescribed asymmetric bending forces on a double cantilever beam (DCB) specimen which contains the interface of interest on the mid-plane. During the experiment the applied bending forces and the corresponding DCB opening displacements are recorded for each fatigue cycle and analyzed for calculating the crack length and the strain energy release rate by using an analytical formula based on the beam on elastic foundation theory. The data are then fed into the closed-loop control program to revise the asymmetric bending forces for the subsequent fatigue cycle such that a constant mode mixity throughout the experiment is ensured. At the end of the experiment the relationship between crack growth rate and the applied strain energy release rate can be obtained by additional post-processing. Experiments had been carried out to investigate the subcritical fatigue crack growth characteristics of an aluminum-epoxy interface under either mode-I or mixed moded conditions. For the particular interface of investigation, the steady-state cyclic fatigue delamination growth is found to display a power-law dependence on the applied strain energy release rate. The measured fatigue growth characteristics may further be incorporated with the fracture mechanics analyses to predict delamination growth on the interface of interest in a realistic structure.

Key words: interface, delamination, fatigue, mixed-mode, double cantilever beam, strain energy release rate

 
INTRODUCTION
There are very limited information available on the interface fatigue delamination growth properties under mixed-moded loading conditions. These subcritical crack propagations are typically driven by residual stresses, thermal cycling, and mechanical or vibrational loading. The desire modeling approach would consist analyzing the interface fatigue crack growth driving forces and comparing them to the experimentally measured crack growth resistance. The fatigue growth rate of a bimaterial interface crack can be evaluated by the strain energy release rate which is related to the mechanical energy released during the separation of the interface. In 1998, Snodgrass et al. [1] found the cyclic fatigue debond growth rate of a polymer-ceramic interface to display a power-law dependence on the applied strain energy release rate, and the interface fracture toughness is strongly dependent of the interface morphology and the thickness of the polymer layer. In 2011, Tumino et al. [2] used standard DCB, End Notched Flexture (ENF), and Mixed Mode Bending (MMB) configurations to test glass fiber (GFRP) and carbon fiber (CFRP) reinforced plastics under pure mode-I, mode-II, and mixed-moded conditions, and found the energy required for delamination of GFRP is higher than that for CFRP. In 2002, Snodgrass et al. [3] studied the subcritical debonding of polymer-silica interface by using DCB and Mixed-Mode Delaminating Beam (MMDB) test configurations. The crack length was continuously measured using compliance relationships and periodically verified. Result of their experiments show that mode-I component has the dominant effect on crack growth properties. In this thesis, we developed a subcritical fatigue delamination growth characterization setup based on mixed-moded bending of a DCB specimen. The experimental system is then applied to study in subcritical growth characteristics of an aluminum-epoxy interface.

The flowchart of the characterization system development is shown in Fig. 1. The process involves defining the system capabilities (measuring interface fatigue crack growth rate under prescribed mixed-moded loading conditions), deducing the analytical data analysis procedure, designing the test system including the loading and measuring components, fixture and sample geometry. A LabVIEW program was written for the test system control. Sensors and actuators used in the system were calibrated individually and then validated at the system level. The system is then applied to study the delamination fatigue growth of an aluminum-epoxy interface.The picture and schematic of the fatigue crack growth characterization system are shown in Figs. 2 and 3, respectively. In Figure 2 A is the PC/ LabVIEW with Data AcQuisition (DAQ) and motion controller for actuator, B is the power supply for sensors and actuators, C is the DAQ connecting block, D is the actuator connecting block, E is the power amplifier for the actuator, F is the actuator, G is the signal conditioner for the loadcell, H: is the signal conditioner for LVDT, and I is the main test frame.
As shown in Fig. 3, the operating flow of the system is such that first the motion controller in PC gives command to the actuator for applying load on the DCB specimen, measurements acquired by loadcells and the linear variable differential transformer (LVDT) are returned back to the LabVIEW program for calculating crack length and strain energy release rate, and then revised loading levels are calculated and send to motion controller for the subsequent loading cycle. The process continues until the test is completed. Shown in Fig. 4 is the flow chart of the LabVIEW control program. To achieve any prescribed loading phase angle for the fatigue crack growth experiment, we could divide the control program into two parts: the first part consists the rise of the cyclic triangle loading profile (UP, UP fix); and the second part is the unloading portion of the triangle wave (Down, Down fix). In the flowchart UP fix and Down fix are the decision making centers.

Figure 1: Design process flow chart

Figure 2: Picture of the test system

Figure 3: Schematic of the test system

Figure 4: Flowchart of the control program

RESULTS AND DISCUSSION

Figure 5: Crack growth rate vs. strain energy release rate for mode I

Figure 6: Crack growth rate vs. strain energy release rate for -30° phase angle

Figure 7: Crack growth rate versus strain energy release rate for -45° phase angle
Results of the aluminum-epoxy interface fatigue delamination growth experiments under prescribed loading mode mixities are shown in Figs 5, 6, and 7. It can be seen from these figures that the exponent of the power-law crack growth rate-strain energy release rate relationship decreases as the absolute value of the phase4 angle increases.

CONCLUSION
For the aluminum-epoxy interface, the subcritical fatigue delamination growth rate is found to to be 10-6 ~10-1 mm/cycle, and has a power-law dependence on the strain energy release rate. Results of this study may be further implemented with fracture mechanics simulations to predict the delamination growth under different phase angles.

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