The goal of this thesis is to develop an experimental setup to evaluate and analyze the effect of crack-parallel stress on the fracture response of materials. In standard fracture test configurations, the crack-parallel normal stress is negligible. However, a new type of experiment, briefly named the gap test, revealed that it was not the case for many quasibrittle and ductile materials. This experiment consists of a simple but new modification of the standard three-point-bend test. Plastic pads with a near-perfect yield plateau are used to generate a constant crack-parallel stress, and the end supports are installed with a gap that closes only when the pads yield. This way, the test beam transits from one statically determinate loading configuration to another, making evaluation easy and accurate. In addition to the gap test, the size effect method, devised in the 1990s, was used to obtain an unambiguous fracture energy based on the geometric scaling of cracked structures with positive geometry. Unlike the work-of-fracture method which measures the total fracture energy on structures of one size, the size effect method was shown in 2014 to give a unique value of the initial fracture energy. It can be widely applied. For quasibrittle materials, i.e. heterogeneous materials consisting of brittle phases, concrete was used as a typical example. The gap test showed that a moderate crack-parallel compressive stress could increase up to ~ 2 times the Mode I (opening) fracture energy of concrete, and reduce it to almost zero when approaching the compressive stress limit. Behavior with a similar trend can be observed within the characteristic length scale, which may be explained by the interplay between friction, interlocking and dilation of microcracks and microsurfaces. To explain this phenomenon, computational models were used, but not all of them could reproduce the results. In particular, the line-crack models, including the basic and enhanced phase-field models with one or two phase variables (PFM), cohesive crack models (CCM), and extended finite element method (XFEM) cannot capture such an effect. The reason lies in the inability of these methods to generate a fracture process zone (FPZ) with {\em finite width}. Consequently, the FPZ (if it exists) is one dimensional and cannot interact with the crack parallel stress.On the contrary, finite elements (FE) or any method that does not confine the energy dissipation within a line in theory can capture the effect of crack -parallel stresses (both in-plane and out-of-plane). However, they must be characterized by a realistic tensorial softening damage model whose vectorial constitutive law captures oriented mesoscale frictional slip, microcrack opening and splitting with microbuckling (i.e. the scalar stress-displacement softening law of CCM and tensorial models with a single-parameter damage law are inadequate). This is best accomplished by the rack band model which, when coupled with microplane model M7, fits the test results satisfactorily. Other standard tensorial strength models such as Drucker-Prager cannot reproduce these effects realistically. Alternatively, one can think of using an equation to describe the dependence of $G_f$ as a function of $\sig_{xx}$ (as well as $\sig_{zz}$ and $\sig_{xz}$ in general). However, this is an approximation that ignores stress tensor history and can only be accepted in some special cases where the crack-parallel stresses are negligible. For {\em ductile materials}, even though the small-scale yielding fracture of plastic-hardening metals (conceived by Hutchinson, Rice and Rosengren) is a well-established theory, their scaling law is not fully understood. Therefore, it must be evaluated before proceeding to the effect of crack-parallel stresses. Unlike the fracture of quasibrittle materials, the fracture of plastic-hardening materials is complicated by a millimeter scale singular yielding zone (YZ) that forms between the micrometer-scale FPZ and the elastic (unloading) material on the outside. Essential for the large-scale transitional size effect is the YZ size, which is here calculated from the condition of equivalence of the virtual works of the plastic-hardening and elastic singular stress fields within the transition zone. The size effect analysis requires taking into account not only the dissipation in the FPZ delivered by the $J$-integral flux of energy through the yielding zone, but also the energies released from the structure and from the unloaded band of plasticized material trailing the advancing yielding zone. Consequently, to describe the transition from micron-size to structure-size specimens (in which both large-scale and small-scale yielding are present), we develop a modified size effect method that includes three asymptotes and requires nonlinear optimization. The size effect law is verified by scaled tests of notched specimens of aluminum. The {\em gap test} is again applied to evaluate the effect of an extrinsically applied $\sig_{xx}$ on the initial fracture energy of aluminum alloy, an example of a ductile material. The ``extrinsic'' nature of $\sig_{xx}$ should be emphasized to highlight the novelty of this work. In fact, the crack parallel stress can arise ``intrinsically'' due to the constraint arising at the tip, which is a result of plastic strain in this area and the geometry of the specimen. This phenomenon was extensively studied in the 1990s by Shih, Hutchinson and many other authors under the name of $J$-$T$ (or $J$-$Q$) theory. To avoid such ``intrinsic'' effect, the thickness, the length-to-depth ratio and the notch length ratio of the specimens in this study were chosen so that such ``intrinsic'' parallel stress can be negligible. Using the size effect method as previously described, it is found that, at crack-parallel stress $\sig_{xx}$ = 40\% of the yield strength, the $G_f$ of aluminum (or $J_{cr}$) is roughly doubled and the $r_p$, which represents collectively the effective radius of the YZ and the characteristic length (or size) of the FPZ, is roughly tripled. To reproduce these results in finite element analysis, one must again consider a realistic tensorial elastic-plastic-damage constitutive law. Such analysis is essential to distinguish the changes in FPZ and in YZ, in which the former must be simulated with a finite width, as in the crack band model. The results in this thesis have broad implications for many materials, e.g., shale, fiber composites, sea ice, foams, bone, and metallic structures that possess the grain boundary comparable to the structural size. These results challenge the century-old hypothesis of constancy of materials fracture energy and set a new paradigm to define the adequacy of the experiments to fully describe the mechanical properties of a material. In addition, these results can be used as a source of validation to evaluate the performance of a damage/fracture model.

Creator

• Nguyen, Hoang Thai

DOI

• https://doi.org/10.21985/n2-yy7y-bb84

Subject

• Engineering

Language

• en

Alternate Identifier

• etdadmin_upload_903421
• http://dissertations.umi.com/northwestern:16100

Date created

• 2022-01-01

Resource type

• Dissertation

Rights statement

• In Copyright