Thesis (MEng)--Stellenbosch University, 2015. / ENGLISH ABSTRACT: The fracture of ductile materials is currently regarded as a complex and challenging phenomenon to characterise and predict. Recently, a bond-based, non-local theory was formulated called the peridynamic theory, which is able to directly solve solid mechanics problems that include fracture. The failure criterion is governed by a critical stretch relation between bonds. It was found in literature that the critical stretch relates to the popular fracture mechanics parameter called the critical energy release rate for predicting brittle linear-elastic failure. It was also proposed that the non-linear critical energy release rate or J-integral can be used to model ductile failure using peridynamics. The aim of this thesis was to investigate the validity of using the J-integral to determine the critical stretch for predicting ductile failure. Standard ASTM fracture mechanics tests on Compact Tension specimens of Polymethyl methacrylate, stainless steel 304L and aluminium 1200H4 were performed to determine the critical energy release rates and non-linear Resistance-curves. Furthermore, a novel peridynamic-based algorithm was developed that implements a critical energy release rate based failure criterion and Digital Image Correlation (DIC) measured full surface displacement fields of cracked materials. The algorithm is capable of estimating and mapping both the peridynamic damage caused by brittle cracking and damage caused by plastic deformation. This approach was used to validate the use of an energy release rate based failure criterion for predicting linear-elastic brittle failure using peridynamics. Also, it showed a good correlation among the test results for detecting plastic damage in the alloys when incorporating the respective J-integral derived critical stretch values. Additionally, Modified Arcan tests were performed to obtain Mode I, Mode II and mixed Mode fracture load results of brittle materials. Mode I peridynamic models compared closely to test results when using the Mode I critical energy release rate, derived critical stretch and served as validation for the approach. Moreover, it was argued that Mode I failure criteria cannot in principle be used to model shear failure. Therefore, it was proposed to rather use the appropriate Mode II and mixed Mode critical energy release rates to predict the respective failures in peridynamics. Also, for predicting ductile failure loads it was found that using a threshold energy release rate derived from the R-curve yielded considerably more accurate failure load results compared to the usage of the critical energy release rate, i.e. J-integral. In this thesis it was shown that there exists great potential for detecting and characterising cracking and failure by using a peridynamic-based approach through coupling DIC full displacement field measurements and the critical energy release rate of a particular structural material. / AFRIKAANSE OPSOMMING: Duktiele breeking van materiale word tans beskou as 'n kompleks- en uitdagende fenomeen om te voorspel en te karakteriseer. 'n Binding-gebaseerde, nie-lokale teorie is onlangs geformuleer, genaamd die peridinamika teorie. Die laasgenoemde stel ons in staat om soliede meganiese probleme met krake direk op te los. Die falings kriterium word bemagtig deur die kritiese strekfaktor tussen verbindings. Daar was bewys dat die kritiese strekfaktor in verband staan met die popul^ere breek meganika parameter, genaamd die kritiese vrylatings-energie-koers vir die voorspelling van bros line^ere-elastiese faling. 'n Onlangse verklaring meen dat die kritiese strekfaktor vir duktiele falingsgedrag, bereken kan word met die nie-line^ere kritiese vrylatings-energie-koers, beter bekend as die J- integraal. Die doel van hierdie tesis was om te meet hoe geldig die gebruik van die J-integraal is om die kritiese strekfaktor te bereken, om sodoende duktiele breking te ondersoek. Standaard ASTM breukmeganika toetse op Polimetilmetakrilat, vlekvrye staal 304L en aluminium 1200H4 is uitgevoer om die kritiese vrylatings-energie-koers en Weerstandskurwes te bepaal. Verder was 'n nuwe peridinamies-gebaseerde algoritme ontwikkel. Die laasgenoemde implementeer die berekening van 'n kritiese strekfaktor, gebaseer op die kritiese vrylatings-energie-koers, sowel as Digitale Beeld Korrelasie (BDK) vol oppervlaks-verplasings veld metings van gebreekte materiale. Dit is in staat om die peridinamiese skade te bereken, tesame met die beeld wat veroorsaak was van bros krake en plastiese vervorming in duktiele materiale. Hierdie benadering is aangewend om die gebruik van 'n vrylatings-energie-koers gebaseerde falings kriterium vir bros line^ere-elastiese falings in peridinamika te bekragtig. 'n Goeie korrelasie tussen toets resultate is ook gevind vir die opsporing van skade wat veroorsaak is deur plastiese deformasie in die legerings waar die onderskeilike J-integrale gebruik was as falings kriteria. Daarbenewens, was Verandere Arcan toetse uitgevoer om die Modes I, Modes II en gemenge Modes falingsresultate te verkry. Die Modes I peridinamiese model het goed vergelyk met die toetsresultate en het gedien as bekragtiging vir die falingsbenaderings. Verder was dit aangevoer dat Modes I falings kriterium in beginsel nie gebruik kan word om skuiffaling te modelleer nie. Dus was dit voorgestel om eerder die toepaslike Modes II en gemengde Modes kritieke vrylatings-energie-koerse te gebruik om onderskeie falings te voorspel in peridinamiese modelle. Dit was ook gevind dat vir die voorspelling van duktiele falingslaste die drumpel vrylatings-energie-koers, wat verkrygbaar is vanaf die Weerstands-kurwe, aansienlik meer akkurate resultate gee, in vergelyking met die gebruik van die kritiese vrylatings-energie-koers, m.a.w. die J-integraal. In hierdie tesis was dit gewys dat daar groot potensiaal bestaan vir die opsporing en karakterisering van krake en falings met 'n peridinamies-gebaseerde benadering, deur dit te skakel met BDK vol verplasings veld metings en die kritiese vrylatings-energie-koers van 'n bepaalde strukturele materiaal.

Significant energy savings can be achieved by improving efficiency of water removal in the press section of a paper machine, rather than energy-intensive evaporative dryer cans. Impulse drying is a novel technology to remove water from the sheet in the press section by using a heated press roll. Delamination is a major challenge to be overcome before impulse drying can be implemented successfully. Delamination is caused by a region of high temperature liquid water under high pressure in the press. Upon exiting the nip, the pressure drops and the high temperature water flashes to steam. If the expansion of the steam is too strong, the bonds between the fibers will fail and a blister will form. The formation of this blister is characteristic of delamination. The goal of this project was to understand the internal mechanics of a wet web as it exits the nip of an impulse dryer. In this way, the components of the sheet can be tailored to open the operating window of impulse drying. A mathematical model, developed to describe the deflection and delamination of an elastic membrane, was utilized in this work. Three failure criteria were employed to represent delamination of this pliable membrane from the more rigid sub layers in the sheet. The experimental portion of this effort was devoted to showing the validity of these models and which was the best fit. A series of experiments were employed to validate the model. A peel test was used to determine the amount of work needed to pull a membrane from a rigid substrate. Pressurized blister experiments were conducted to find the relationship between critical pressure and initial defect size. The predictions from the mathematical model were then compared to these experimental values. Finally, work was done to understand the physics of the delamination of a porous membrane.

Double cantilever beam (DCB) specimens with distinct intermetallic microstructures and different geometries were fractured under different mode ratios of loading, ψ, to obtain critical strain energy release rate, Jc. The strain energy release rate at crack initiation, Jci, increased with phase angle, ψ, but remained unaffected by the joint geometry. However, the steady-state energy release rate, Jcs, increased with the solder layer thickness. Also, both the Jci and Jcs decreased with the thickness of the intermetallic compound layer. Next, mode I and mixed-mode fracture tests were performed on discrete (l=2 mm and l=5 mm) solder joints arranged in a linear array between two copper bars to evaluate the J = Jci (ψ) failure criteria using finite element analysis. Failure loads of both the discrete joints and the joints in commercial electronic assemblies were predicted reasonably well using the Jci from the continuous DCBs. In addition, the mode-I fracture of the discrete joints was simulated with a cohesive zone model which predicted reasonably well not only the fracture loads but also the overall load-displacement behavior of the specimen. Additionally, the Jci calculated from FEA were verified estimated from measured crack opening displacements in both the continuous and discrete joints. Finally, the pad-crater fracture mode of solder joints was characterized in terms of the Jci measured at various mode ratios, ψ. Specimens were prepared from lead-free chip scale package-PCB assemblies and fractured at low and high loading rates in various bending configurations to generate a range of mode ratios. The specimens tested at low loading rates all failed by pad cratering, while the ones tested at higher loading rates fractured in the brittle intermetallic layer of the solder. The Jci of pad cratering increased with the phase angle, ψ, but was independent of surface finish and reflow profile. The generality of the J =Jci(ψ) failure criterion to predict pad cratering fracture was then demonstrated by predicting the fracture loads of single lap-shear specimens made from the same assemblies.

Double cantilever beam (DCB) specimens with distinct intermetallic microstructures and different geometries were fractured under different mode ratios of loading, ψ, to obtain critical strain energy release rate, Jc. The strain energy release rate at crack initiation, Jci, increased with phase angle, ψ, but remained unaffected by the joint geometry. However, the steady-state energy release rate, Jcs, increased with the solder layer thickness. Also, both the Jci and Jcs decreased with the thickness of the intermetallic compound layer. Next, mode I and mixed-mode fracture tests were performed on discrete (l=2 mm and l=5 mm) solder joints arranged in a linear array between two copper bars to evaluate the J = Jci (ψ) failure criteria using finite element analysis. Failure loads of both the discrete joints and the joints in commercial electronic assemblies were predicted reasonably well using the Jci from the continuous DCBs. In addition, the mode-I fracture of the discrete joints was simulated with a cohesive zone model which predicted reasonably well not only the fracture loads but also the overall load-displacement behavior of the specimen. Additionally, the Jci calculated from FEA were verified estimated from measured crack opening displacements in both the continuous and discrete joints. Finally, the pad-crater fracture mode of solder joints was characterized in terms of the Jci measured at various mode ratios, ψ. Specimens were prepared from lead-free chip scale package-PCB assemblies and fractured at low and high loading rates in various bending configurations to generate a range of mode ratios. The specimens tested at low loading rates all failed by pad cratering, while the ones tested at higher loading rates fractured in the brittle intermetallic layer of the solder. The Jci of pad cratering increased with the phase angle, ψ, but was independent of surface finish and reflow profile. The generality of the J =Jci(ψ) failure criterion to predict pad cratering fracture was then demonstrated by predicting the fracture loads of single lap-shear specimens made from the same assemblies.