Deformation and Structure-Property Relations of Paper During Mode I Steady-State Crack Growth

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Paluskiewicz, Sarah A.
Muhlstein, Christopher L.
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Paper and pulp fiber-based materials have experienced an expansion in use from commodity applications (such as shipping containers) to integration into medical devices. Understanding how cracks form and grow allows for more reliable tear, such as in perforated papers, or for engineered crack growth resistance, such as prevention of web breaks or product failures. As a thin-sheet material, the effectiveness of single-parameter fracture mechanics crack tip parameters (K and J) break down because of early gross plasticity. But the thin-sheet nature of the material justifies plane stress assumptions which allow the surface response to embody the full specimen response. Therefore, this work uses non-contact digital image correlation to create and expand empirical knowledge of Mode I growing, quasi-static, steady-state, cracks in machine-made paper. The mechanical response of paper's heterogeneous network structure is complex and includes anisotropy, non-affinity, and visco-elasticity. However, I employ an incremental strain framework to characterize each evolution of unique strain response. Strategically-placed incremental strain measurements of the full-field specimen surface illuminated the three-stage process from early gross plasticity to a transition to contained zones of active plasticity (ZAPs) in steady-state, which concluded in a final fast fracture of a small remaining ligament. At overload, there was a non-zero offset stress from the operating fracture mechanisms of crack bridging and fiber pull-out. I use a thresholding scheme tied to the uniaxial fracture strain to measure the fibrous crack tip. Crack growth accelerated (with respect to crosshead displacement) in early transitional growth, then reached constant velocity (again, with respect to crosshead displacement) at steady-state. I show three singular ZAPs that drive steady-state crack growth: 1) a primary axial ZAP, 2) a secondary ZAP of reversed plasticity, and 3) a primary ZAP of negative transverse strain. In addition, I identify non-singular shear strains and rotation at the forming crack. I use relative humidity to adjust the constitutive relationships and separate the effects of mechanical orthotropy from structural orthotropy. I found that the primary axial and transverse ZAPs and rotation lobes scaled with increased relative humidity, suggesting they were sensitive to the network inter-fiber bonding. The reversed zone remained invariant in size and had a weaker singularity strength because the fiber network was previously damaged in the crack formation process. In addition as the relative humidity was increased, the characteristic and offset stresses of steady-state crack growth decreased about the amount as the uniaxial ultimate tensile stress. Lastly, I measure the exact sequence of strain and rotation that form a steady-state crack, which featured a local maximum of axial strain and a local minimum of transverse strain at crack formation then shear and rotation. By defining all the active incremental process zones during steady-state crack growth, I have created a more complete mechanistic description to serve as a foundation for more effective models of growing, steady-state cracks.
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