Cushion Package System Design and Numerical Simulation of Expanded Polypropylene（EPP）

產品物流在運輸過程中，都必定會承受搬運輸送的風險，例如摔落、擠壓等，透過緩衝包裝系統可以有效減少產品在物流期間外界意外輸入之衝擊力，避免損壞產品以保持原有的形狀及品質。由於在緩衝包裝系統的各項評估試驗中，以落下所造成的衝擊最為劇烈。又以往傳統皆以準靜態應力—應變曲線為基礎去模擬分析，當中並未考慮當材料具應變率效應時之影響，故本研究以發泡式緩衝包裝系統，主要是發泡聚丙烯（EPP）的自由落下試驗，考慮應變率效應以及加入能量損失的考量來進行數值模擬，用以評估緩衝包裝材料之功效，取代傳統以試誤法設計包裝系統之方式。 文獻上對於包裝系統設計之相關研究大多都忽略緩衝包裝材料之應變率效應以簡化數值模擬，對於EPP之研究就更少。所以本文的主旨在於透過準靜態壓縮試驗、高速動態衝擊試驗及自由落下試驗和數值模擬瞭解EPP在掉落測試試驗中的行為，並用以評估其包裝效果；同時考慮應變率效應對緩衝包裝材料行為之影響，考量應變率效應與能量損失間的關係，以便更貼近於真實自由落下過程中碰撞之數值模擬。 本研究在數值模擬中所使用之材料組成律為對EPP進行一系列準靜態壓縮試驗與高速動態衝擊試驗，並提出一應變率相依之材料組成律模型把材料之應變率相依特性表示成數學解析式，以便於數值模擬，甚至於真實產品之緩衝包裝系統設計上可以更準確的模擬真實自由落下碰撞之力學行為。此外，本研究亦利用高速攝影機拍攝觀察真實自由落下行為，配合加速度規量測之加速度歷時反推出真實行為下之應力—應變曲線，另外以高速動態衝擊試驗驗證反推之結果，最後證實EPP如文獻所述是具有應變率效應的，並歸納出考慮應變率效應下之能量損失。本研究也將不同的試驗結果整理並歸納出考慮應變率效應與否之能量損失，並以靜態評估曲線法及考慮應變率效應與否的單自由度非線性彈簧系統預測自由落下之碰撞結果。 於緩衝包裝材料微結構方面，使用光學式電子顯微鏡（OEM）及掃瞄式電子顯微鏡（SEM）觀察EPP之微結構，瞭解其微結構是否使材料具應變率效應的一個重要因素。 最後，對於實際產品設計而言，本研究先整理出EPP之應變能密度設計於材料之適用範圍，再透過本研究考慮應變率效應與否之數值模擬方法，來預測實際產品在自由落下時的最大加速度值、最大應變甚至於真實應力—應變曲線，繼而與真實自由落下試驗的結果作比較，以驗證本研究考慮應變率效應的數值模擬方法之可行性與準確性。Products bear a lot of risks of getting damaged because of falling, getting compressed, etc. during transportation of logistics. In order to preserve products shape and quality, we can reduce the impact force during the logistics using packaging system. In general, we consider that packaging materials would not exhibit the strain rate effect while we predict free drop test results. In other words, the quasi-static compression stress-strain curve is used to simulate the results. But some packaging materials probably have the strain rate effect. Therefore, the foam packaging system of free drop test in this research considers the strain rate effect, that is the packaging materials are strain rate dependent. The energy loss is also considered into account when using numerical simulation methods to predict the maximum acceleration. The aim of this research is to understand the behavior of foam packaging materials during free drop by numerical simulation methods. Most of the literature on relevant research of foam packaging system neglects the strain rate effect to simplify the numerical simulation. But in this research it is shown that the strain rate effect would influence the maximum strain captured by high speed camera, even if there is no difference between free drop test and numerical simulation on maximum acceleration if the strain rate effect is not considered. So this research generalizes some experimental results to coordinate the relationship between the strain rate effect and the energy loss. Later, both energy method and single degree-of-freedom of nonlinear spring system are used to predict the results from free drop test. The constitutive law of foam packaging materials used in this research, for example expanded polypropylene (EPP), is constructed by series of quasi-static compression test and high-rate dynamic impact test. A numerical material constitutive law model considering the strain rate effect is also published to simulate the strain rate dependent property about EPP. We can accomplish the aim, considering the strain rate effect is used in this model when we are simulating the results, and to develop the numerical simulation which can predict maximum strain more accurately. In addition, for verifying that EPP has the strain rate effect, the high speed camera cooperated with the accelerometer through free drop test is used to derive the actual stress-strain curve of EPP packaging system. Finally, the fact that EPP is strain rate depenedent material has been proved. The microstructure photos of EPP by both optical electron microscope (OEM) and scanning electron microscope (SEM) were captured. This research also attempts to understand the relationship between strain rate effect and the microstructure of EPP. Furthermore, for designing EPP packaging system of real products, the appropriate range of strain energy density of EPP was chosen. The maximum acceleration, maximum strain and actual stress-strain curve of free drop test are predicted by numerical simulation methods considering the strain rate effect or not. To conclude, the results by several numerical simulation methods and free drop test are compared to explain that these methods which considers strain rate effect are feasible and accurate