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Dynamic crack initiation, growth and branching phenomena are comprehensively investigated in soda-lime glass using a vision-based method, Digital Gradient Sensing (DGS), in conjunction with digital ultrahigh-speed photography. Being a high-stiffness and low-toughness structural material, soda-lime glass poses enormous temporal and spatial challenges to opto-mechanical measurements using legacy techniques. Unlike the past works on indirect evaluation of instantaneous stress intensity factors in glass via crack speed, DGS is capable of direct quantification of both crack-tip fields and crack speeds. This is useful for examining the dynamic fracture characteristics such as pre- and post-crack initiation histories, crack initiation toughness, energy release rate (Gd)-apparent velocity (V) variation, and to shed light on crack bifurcation phenomenon. Accordingly, directly measured mixed-mode stress intensity factor histories and crack-tip velocity histories at branching and subsequent growth are reported. These are supplemented with Gd–V plots which show certain unique signatures at branching. From the measured fracture parameters, a material length characteristic based on microcracking due to normal stress in the crack growth direction ahead of the propagating crack that triggers branching is advanced.

Mechanical characterization of transparent graft Interpenetrating Polymer Networks or graft-IPNs based on polyurethane and acrylic copolymer are reported under both quasi-static and dynamic loading conditions. This study builds on an earlier work detailing the synthesis of the graft-IPNs [1]. Optically transparent graft-IPNs were synthesized using elastomeric polyurethane (PU) phase and stiff acrylate-base copolymer (CoP) phase. The ratios of CoP:PU were varied from 90:10 up to 60:40 by weight. Two grades of graft-IPNs were synthesized by using 650 g mol−1 and 1400 g mol−1 poly (tetramethylene ether) glycol (PTMG) during synthesis to study the molecular weight effect. Quasi-static tensile and fracture tests as well as dynamic fracture tests were performed. The dynamic fracture tests were carried out at high strain rate using a modified-Hopkinson pressure bar in conjunction with an optical technique called Digital Gradient Sensing (DGS) and ultrahigh-speed photography. Quasi-static tests indicate significant enhancements in crack initiation toughness and change in failure mode (brittle to ductile) when the constituents were varied. Enhancements in crack inititation toughness were also observed under dynamic loading. These results were further compared with those for commercial poly (methyl methacrylate) (PMMA) and polycarbonate (PC) sheet stock. Further improvement in fracture properties were observed under quasi-static loading conditions with increase in molecular weight of PTMG. The relatively high values of fracture toughness obtained for graft-IPNs is attributed to the crosslinks generated between the CoP and PU networks.

Transparent brittle ceramics such as soda-lime glass pose unique challenges for performing full-field optical measurement of deformations and stresses to characterize fracture and failure behaviors. Low fracture toughness coupled with high stiffness and elastic wave speeds are among the factors responsible for some of these challenges as deformations tend to be confined to an extremely small region near an almost mathematically sharp growing crack. Need for strong birefringence, elaborate optics, or lack of sufficient measurement sensitivity are some of the factors against legacy techniques such as photoelasticity, optical interferometry, and speckle methods, respectively, to study soda-lime glass. Motivated by these factors, the feasibility of digital gradient sensing (DGS) method to measure impact induced deformations near a contact-point and a dynamically growing crack-tip in soda-lime glass are demonstrated in this work. This second of a two-part paper demonstrates the applicability of DGS for the problems under stress wave loading conditions. Ultrahigh-speed photography (1 million frames per sec) in conjunction with DGS and a Hopkinson pressure bar to load soda-lime glass specimens are employed. The optical measurements are postprocessed to obtain relevant engineering parameters and stress field σx+σy near dynamically loaded crack-tip, both while stationary and during propagation.

Mixed-mode dynamic crack initiation and growth in polymethymethacrylate (PMMA) and polycarbonate (PC) are studied experimentally. A simple specimen geometry in conjunction with a dynamic loading configuration to generate different mode-mixities at crack initiation is demonstrated. A Hopkinson pressure bar is used to rapidly load free-standing edge cracked samples in a reverse impact configuration. By eccentrically loading the specimen relative to the crack line, various mode-mixities at crack initiation are achieved by increasing the initial crack length while keeping all other experimental parameters the same. A relatively new full-field optical technique, Digital Gradient Sensing (DGS), along with high-speed photography is used to perform full-field measurements. DGS measures instantaneous angular deflections of light rays representing two orthogonal stress gradients under plane stress conditions. The mode-I and -II stress intensity factor histories are evaluated via over-deterministic least-squares analysis of optically measured data. By quantifying the critical stress intensity factors evaluated at crack initiation, dynamic fracture envelopes are developed for both the polymers. The results are studied comparatively and relative to the brittle fracture criteria. From measured stress intensity factors and crack speeds in the post-initiation regime, energy release rate vs. velocity plots for different mixed-mode configurations are produced for both the polymers.

In this paper, the dynamic crack-interface interactions and the related mechanics of crack penetration vs. branching at a weak interface are studied experimentally. The interface is oriented perpendicular to the incoming mode-I crack in an otherwise homogeneous bilayer. The focus of this investigation is on the effect of interface location and the associated crack-tip parameters within the bilayer on the mechanics of the ensuing fracture behavior based on the optical methodologies laid down in Ref. Sundaram and Tippur (2016). Time-resolved optical measurement of crack-tip deformations, velocity and stress intensity factor histories in different bilayer configurations is performed using Digital Gradient Sensing (DGS) technique in conjunction with high-speed photography. The results show that the crack path selection at the interface and subsequently the second layer are greatly affected by the location of the interface within the geometry. Using optically measured fracture parameters, the mechanics of crack penetration and branching are explained. Counter to the intuition, a dynamically growing mode-I approaching a weak interface at a lower velocity and stress intensity factor penetrates the interface whereas a higher velocity and stress intensity factor counterpart gets trapped by the interface producing branched daughter cracks until they kink out into the next layer. An interesting empirical observation based on measured crack-tip parameters for crack penetration and branching is also made.

Transparent brittle materials such as soda-lime glass (SLG) with relatively low fracture toughness and high stiffness pose unique challenges for performing full-field optical measurement of deformations and stresses to characterize their fracture behavior. The current work builds on authors’ previous report wherein the feasibility of Digital Gradient Sensing (DGS) was demonstrated for measuring stress wave induced crack-tip deformations in SLG. In this study, ultrahigh-speed photography (>1 million frames per sec) was used in conjunction with DGS and a Hopkinson pressure bar to load V-notched SLG plates to investigate the crack branching phenomenon. The experimental parameters were controlled such that a single mode-I crack that initiated at the V-notch tip propagated through the glass plate before branching into two prominent mixed-mode daughter cracks. The optical measurements of angular deflection fields that represent stress gradients in two orthogonal in-plane directions were obtained. Using higher order finite-difference based least-squares integration (HFLI) scheme, stress invariant fields (σxx + σyy) were evaluated near dynamically propagating crack-tip throughout the branching process.

IPNs are made of two or more polymer networks, each polymerized in the presence of the other/s. They can be suitable alternatives to traditional polymers made from single monomer as desirable characteristics of the constituent polymers can be engineered into IPNs. In this study, an acrylic-based transparent graft Interpenetrating Polymer Networks or simply graft-IPNs were processed and their mechanical properties in general and fracture/failure behaviors in particular were characterized. Good optical transparency, high fracture toughness, and high stiffness were among the attributes targeted in the graft-IPNs for potential transparent armor applications. The graft-IPNs were synthesized by sequential polymerization of compliant elastomeric polyurethane (PU) phase and a stiff acrylate-based copolymer (CoP) phase to generate crosslinks (or, ‘grafts’) between the two networks. A series of such graft-IPNs were synthesized by varying the ratios of CoP:PU. Uniaxial tension tests were performed on the resulting IPNs to measure the elastic modulus and strength whereas mode-I fracture toughness was measured under both quasi-static and dynamic loading conditions. A Hopkinson pressure bar was used in conjunction with an optical technique called Digital Gradient Sensing (DGS) and ultrahigh-speed photography to measure the fracture behavior during stress wave loading. The results show significant enhancements in the crack initiation toughness for some of the graft-IPN compositions relative to the constituents as well as commercially procured PMMA and polycarbonate (PC) sheet stocks. Besides the optical transparency, the increase in fracture toughness is attributed to the grafts or crosslinks generated between the PU and CoP networks.

Glass-Ceramics (GCs) find wide applications in electronic packaging, kitchenwares, optics, acoustic systems, aerospace industry, as armor materials, and as aesthetic material for dental restoration due to their simple processing, easy machinability, low porosity and high strength.. However, they are inevitably subjected to tensile load resulting in catastrophic failure due to their sometimes low fracture toughness and high brittleness. In this context, a zirconia containing lithium disilicate glass ceramic is developed and mechanically characterized. Its fracture toughness and hardness are measured using Chevron Notch Short Bar (CNSB) method and Vickers indent respectively.. Further, the material was subjected to single edge notched bar (SENB) loading in 3-point bend configuration. The non-linearity in the load-deflection curve suggested the presence of R-curve behavior which was subsequently measured. The results of this technique are compared with those of Corning Ultra Low Expansion (ULE) glass, which was used as a standard for the measurement. In the glass-ceramic material a rising R-curve, a desirable attribute as it suppresses subcritical crack growth, was evident. With higher fracture toughness, rising R-curve and improved brittleness index, this GC has advantaged mechanical attributes. Further, the fracture surface exhibited significant roughness as compared to ULE glass. With multiple potential factors contributing to the improved fracture toughness, each of their contributions is yet to be fully understood.

Highly transparent and tough graft-interpenetrating polymer networks (graft-IPNs) were synthesized using an elastomeric polyurethane phase (PU) and a highly stiff acrylate-base copolymer phase. The grafting points between the two networks were generated with the purpose of minimizing the phase separation process of the polymeric systems. In order to generate the grafting between the networks, an acrylic resin capable of undergoing both free radical and poly-addition poly- merization was employed. The thermo-mechanical properties, fracture toughness properties as well as network and surface phase morphology of the graft-IPNs synthesized were evaluated in this work. Data obtained suggested that the minimiza- tion of the phase separation was achieved by the generation of crosslinking points between both networks. High trans- parency was obtained in all samples as an indication of the high level of interpenetration achieved. The relative high values obtained for the fracture toughness tests suggest that generating chemical crosslinks between networks is a good approach for increasing the fracture toughness of polymeric materials.

Transparent ceramic materials such as soda-lime glass pose unique challenges for visualizing and quantifying deformations to characterize fracture and failure. The relatively low fracture toughness coupled with high stiffness and elastic wave speeds create spatio-temporal challenges as deformations tend to be confined to a very small region around an almost mathematically sharp crack that tends to propagate at ∼1500 m/s. Soda-lime glass show weak birefringence to be able to use conventional photoelasticity. Interferometric methods often need elaborate coherent optics and are less attractive in terms of experimental simplicity. Digital image correlation (DIC) techniques, on the other hand, require creating speckles on the specimen surface which makes it difficult to locate a propagating crack-tip for evaluating fracture parameters precisely. Also, achieving a good measurement resolution at conventional magnifications using currently fielded high-speed cameras is difficult. Motivated by these overlapping factors, the feasibility of Digital Gradient Sensing (DGS) method to measure crack-tip deformations near stationary and growing cracks in soda-lime glass is investigated in this work. Both quasi-static and dynamic problems associated with crack initiation and growth are successfully demonstrated.

Mixed-mode dynamic crack initiation and growth in polymethymethacrylate (PMMA) and polycarbonate (PC) are studied experimentally. A simple specimen geometry and loading configuration is used to generate various mode-mixities during dynamic crack initiation and fracture. A Hopkinson pressure bar is used to rapidly load free-standing edge cracked samples in reverse impact configuration. Using eccentric loading relative to the crack line, different mode-mixities at crack initiation are achieved by increasing the initial crack length while keeping all other experimental parameters unchanged. A relatively new full-field optical technique, Digital Gradient Sensing (DGS), along with ultrahigh-speed photography is used to perform full-field measurements. DGS can measure instantaneous angular deflections of light rays due to elasto-optic effects and provides two orthogonal stress gradients under plane stress conditions. The mode-I and -II stress intensity factor histories of PMMA are evaluated via overdeterministic analysis of optically measured data. By quantifying critical stress intensity factors evaluated at crack initiation, dynamic fracture envelopes can be developed.

Dynamic fracture behavior of layered PMMA sheets is studied using transmission-mode Digital Gradient Sensing (DGS) technique. DGS is a relatively new optical method that exploits elasto-optic effects exhibited by transparent solids allowing a direct quantification of two orthogonal in-plane stress gradients simultaneously and hence crack tip parameters when used to study fracture mechanics problems. The current work builds on authors’ previous two reports on this topic. Interfacial trapping, bifurcation and mixed-mode penetration into the second layer of a dynamically growing mode-I crack in the first layer encountering a normally oriented interface in a bi-layered configuration was reported in the first report [1]. In the second, the role of the location of a weak interface relative to the initial crack tip within the given geometry of the specimen was studied and interfacial penetration vs. bifurcation mechanisms was demonstrated and analyzed [2]. The current work focuses on the effect of impact velocity and the resulting loading rate on crack branching/penetration phenomenon when the mode-I crack encounters a normally oriented interface. In this ongoing work, a select location of interface relative to the initial crack tip is re-examined by varying the impact velocity. Using DGS for visualization and quantification, fracture mechanisms associated with crack growth are explained for the bi-layered system.

Shape and surface topography evaluation from measured orthogonal slope/gradient data is of considerable engineering significance since many full-field optical sensors and interferometers readily output such a data accurately. This has applications ranging from metrology of optical and electronic elements (lenses, silicon wafers, thin film coatings), surface profile estimation, wave front and shape reconstruction, to name a few. In this context, a new methodology for surface profile and stress field determination based on a recently introduced non-contact, full-field optical method called digital gradient sensing (DGS) capable of measuring small angular deflections of light rays coupled with a robust finite-difference-based least-squares integration (HFLI) scheme in the Southwell configuration is advanced here. The method is demonstrated by evaluating (a) surface profiles of mechanically warped silicon wafers and (b) stress gradients near growing cracks in planar phase objects.