Non-essential Work Research Articles

Influence of temperature on plane stress ductile fracture of poly(ethylene terephthalate) film

Double edge notched poly(ethylene terephthalate) (PET) specimens of varying ligament lengths and 0·125 mm thickness have been pulled to complete fracture between 23 and 160°C. Within this temperature range, propagation of the crack was always stable, producing load–displacement curves at various ligament lengths that were geometrically similar to one another. Essential work of fracture (EWF) analysis was used to study the effect of temperature on fracture toughness. A linear relationship was obtained between specific total work of fracture Wf and ligament length over the entire temperature range under consideration. The slope of the line, which is termed specific non-essential work of fracture βwp , showed a maximum near the glass transition temperature of the material (Tg ≈ 93°C). Beyond this point, βwp decreased sharply with increasing temperature. The intercept of the line at zero ligament length, which is referred to as specific essential work of fracture we , showed three types of variation with respect to temperature. Below Tg , we was found to be more or less independent of temperature; above Tg it increased with temperature and reached a maximum value at the end of the leathery region (∼120°C); beyond which it decreased steadily.

Work of fracture of polystyrene/high density polyethylene blends compatibilized by triblock copolymer

The fracture toughening behavior of polystyrene/high density polyethylene blends compatibilized by 10 wt % of a styrene-ethylene-butylene-styrene triblock copolymer (SEBS) was assessed using single-edge notched tension (SENT) and double-edge notched tension (DENT) specimens of various gauge lengths over a wide range of tensile rates. The fracture of DENT and SENT specimens was completely ductile under the plane-stress condition. A linear relationship was observed between the specific total work of fracture and the ligament length (L) for a given L range. The results showed that the essential work (w e ) was independent of the tensile rate (R) range of 1-30 mm/min, and it then decreased considerably when R was increased to 50 mm/min and above. However, the nonessential work exhibited a rate independent trend behavior. In addition, w e and the specific nonessential work of fracture (βw p ) were basically independent of the gauge length (G), provided that G was greater than the width of the sample. Finally, it was also shown that the w e and βw p values for SENT specimens are obviously greater than those for DENT specimens.

Temperature dependence of essential and non-essential work of fracture parameters for polycarbonate film

Single edge and double edge notched polycarbonate specimens of thickness 0·;375 mm have been pulled to complete fracture at temperatures between 25 and 120°C. Within this temperature range specimens underwent full ligament yielding prior to final fracture, producing load–displacement curves at various ligament lengths that were geometrically similar to one another for a specific geometry. On the basis of these, the method of the essential work of fracture was used to study the effect of temperature on fracture toughness of polycarbonate film. Results showed that a linear relationship exists between specific total work of fracture wt and ligament length L over the entire temperature range under consideration. The slope of the line, which is referred to as the specific non-essential total work of fracture βwp , increased with increasing temperature. However, the interception at L = 0, which is referred to as the specific essential total work of fracture we , showed little variation with respect to temperature. Change of geometry affected both values, although the change in βwp was more significant than that of we , for which change of no more than 10%was attained. Based on the maximum load on the load–displacement curve, wt for double edge notched specimens was partitioned into the specific work of fracture for yielding wy and the specific work of fracture for yielding necking/tearing wnt . Linear relationships were found for both terms as a function of ligament length from which the essential (we,y , we,nt ) and non-essential (βy wp,y , βnt wp, nt ) related work terms were attained. Results showed that the yielding related work terms for polycarbonate decrease, while the necking/tearing related work terms increase, with increasing temperature.

Molecular dependence of the essential and non-essential work of fracture of amorphous films of poly(ethylene-2,6-naphthalate) (PEN)

Plane stress fracture toughness of amorphous films of poly(ethylene-2,6-naphthalate) (PEN) with various molecular weights (MW; characterized by the intrinsic viscosity, IV) was determined by the essential work of fracture (EWF) concept using tensile-loaded deeply double-edge notched (DDEN-T) specimens. These PENs met the basic requirement of the EWF concept: full ligament yielding, which was marked by a load drop in the force–displacement curves of the DDEN-T specimens, preceded the crack growth. This “load mark” allowed us to partition between yielding and necking. The yielding-related EWF terms were not affected by the MW of the resins and thus served for the comparison of the results. It is argued that the EWF response is governed by the entanglement network density. The role of entanglements was substantiated by showing that the “plastic” zone developed via cold drawing and not by true plastic deformation. On the other hand, MW influenced the necking related EWF terms. High MW PENs failed by stable crack growth, whereas low MW resins experienced unstable crack growth (more exactly a transition from stable to unstable crack growth) in the necking phase. This was traced to the load distribution capacity of the long entangled chains. Attempts were also made to estimate the essential and non-essential work of fracture parameters and their constituents from uniaxial tensile tests performed on dumbbells.

Temperature and deformation rate dependence of the work of fracture in polycarbonate (PC) film

Single edge notched polycarbonate (PC) specimens of thickness 0.175 mm were pulled to complete fracture at temperatures between 25°C and 100°C and at loading rate values of 2, 5 and 50 mm/min. A duckbill-shaped yielded zone was formed ahead of the crack tip in all the specimen tested. Propagation of the crack within the yielded zone was always stable. The method of essential work of fracture (EWF) was used to study the effects of temperature and loading rate on fracture toughness. The specific essential work of fracture, w e, was found to be independent of both temperature and loading rate. The non-essential work of fracture, βw p, increased with increasing temperature but showed no systematic variation with respect to loading rate. Moreover, plastic constraint factor, m, also increased with increasing temperature. A linear temperature dependence was obtained for both βw p and m giving the extrapolated values of βw p = 0 and m = 0.5 at −23°C.

Deformation rate dependence of work of fracture parameters in polybutylene terephthalate (PBT)

AbstractEssential work of fracture (EWF) analysis was used to study the effect of loading rate (v = 2, 5, 25 and 50 mm/min) on fracture toughness of PBT film of thicknesses 0.175, 0.275, 0.375 and 0.5 mm. Using single edge notched tension (SENT) specimens, it was found that the specific essential work of fracture, we, increases slightly with increasing loading rate but Within the specified range of loading rate, it showed no significant variation with respect to thickness. The specific non‐essential work of fracture, βwp, decreased with increasing rate and increasing thickness.

Fracture characterization of low-density polyethylenes by the essential work of fracture: Changes induced by thermal treatments and testing temperature

The tensile deformation and fracture behavior of commercially available low-density polyethylene (LDPE) films, having different molecular characteristics, was studied. Submitting samples to specific thermal histories controlled the morphological structure of these semicrystalline polymers. Phase-structure analysis of the resulting materials was performed by DMA and DSC analyses. The plane-stress essential work of fracture methodology was chosen because the materials used had failed after complete necking of the remaining ligament. Significant differences in behavior, induced by thermal treatments, were found for the tensile yield stress and the specific nonessential work of fracture, but not in the specific essential work of fracture. The results show that the mechanical properties and fracture behavior depend not only on the crystallinity levels and molecular weight characteristics of the samples, but also upon the degree of structural continuity. The β-relaxation process, associated with the crystal-amorphous interphase, strongly influences the fracture behavior at testing temperatures chosen below the β-relaxation temperature. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 74: 781–796, 1999

Factors affecting work of fracture of uPVC film

Essential work of fracture (EWF) approach was used to evaluate the fracture toughness of uPVC film. It was found that the specific essential work of fracture, (we) is independent of specimen width, specimen gauge length, loading rate and test temperature, but dependent on the geometry of the test specimens. Test temperature and geometry were the only testing parameters affecting the specific non-essential work of fracture (βwp) in a very significant way. The plastic zone shape factor (β) was found to be very sensitive to both the geometry and temperature. It was established that both we and βwp could be partitioned into components that are linked to yielding (i.e. we,y and βywp,y) and necking/tearing (i.e. we,nt and βntwp,nt) processes. The only testing parameter that affected we,y was test temperature, whereas we,nt was affected by test temperature as well as geometry. All testing parameters used in this study affected the values of βywp,y and βntwp,nt.

Fracture behaviour of polypropylene/glass bead elastomer composites by using the essential work-of-fracture method

The plane-stress static fracture response of blends composed of isotactic polypropylene glass beads (GBs) and an elastomer of styrene/ethylene–butylene/styrene type (SEBS) in both the ungrafted state and the grafted state with maleic acid anhydride (SEBS-g-MA) was studied at room temperature and v=1 mm min-1 cross-head speed. The volume fraction of GBs was kept constant (10 vol%) whereas that of the elastomer was set for 5 and 20 vol%, respectively. Deeply double edge-notched specimens of different ligaments were cut from pressed sheets of about 1 mm thickness and subjected to tensile tests at ambient temperature. The development of the plastic and process zone was studied in situ, i.e., during loading of the specimens, by light microscopy and infrared thermography. From the specific work of fracture versus ligament length plots, the essential and non-essential work of fracture components were determined. It was established that the essential work-of-fracture approach works well for these hybrid composites. The specific essential work of fracture, we, increased with increasing amount of the rubbery modifier but depended on its type. Grafting changed the morphology of the composites (SEBS-g-MA covered the GBs, whereas SEBS was present as an additional dispersed phase) and affected both the essential (slightly) and the non-essential or plastic work (considerably) terms. It was established that SEBS-g-MA is a less efficient toughener than SEBS because of the substantial differences in the related failure modes. © 1998 Chapman & Hall

Thickness dependence of work of fracture parameters of an amorphous copolyester

The fracture toughness of an amorphous copolyester (COP) of different sheet thickness (0.5, 3 and 6 mm) was determined by the essential work of fracture (EWF) concept using tensile-loaded deeply double-edge notched (DDEN-T) specimens. It was shown that this COP meets the basic requirement of the EWF concept, viz. full ligament yielding (marked by a load drop in the load-displacement curve) prior to the crack growth, in the thickness range studied. Based on the well-resolved yielding both the specific essential (we) and non-essential work of fracture (wp) were split in the contributing terms related to yielding (wI), and necking and fracture (wII). It was found that we is likely to be independent on the thickness range when plane stress conditions prevail, and thus represents a material parameter. This finding is at odds with previous results suggesting that we is thickness dependent. The development and size of the plastic zone were studied by light microscopy and infra-red thermography. The latter technique overestimated the plastic zone in thicker sheets by not differentiating between pure and diffuse yielding. © 1997 Elsevier Science Ltd.

For what kind of polymer is the toughness assessment by the essential work concept straightforward?

The essential work of fracture (EWF) concept seems to be a proper and easy way to determine the inherent fracture behavior of ductile polymers. Unfortunately, all experiments reported until now were performed on polymers which did not meet the basic requirement of this fracture mechanical approach, viz. full ligament yielding prior to onset of crack growth. This problem often resulted in wrong conclusions and useless discussions on the specimen preparation, including notching techniques. By using tensile-loaded deeply double-edge notched (DDEN-T) specimens of amorphous copolyesters (aCOP) it was demonstrated that they are, in fact, the optimum choice to push forward the EWF concept for ductile polymers. Full ligament yielding before crack growth was evidenced by infrared thermographic (IT) frames taken during the loading of the DDEN-T specimens. The yielding “marked” with a load-drop in the corresponding load-displacement curves, enabled to split both the specific essential and non-essential work of fracture into their contribution terms: yielding and necking incl. fracture, respectively. It was argued that this EWF approach is most straightforward for the toughness description of such amorphous polymers that undergo necking by (multiple) shear banding without considerable strain-hardening, as aCOPs do.

On the essential and non-essential work of fracture of biaxial-oriented filled PET film

Abstract The plane-stress fracture toughness of a biaxial-oriented, filled poly(ethylene terephthalate) (BOPET) film was determined by the essential work of fracture concept using tensile-loaded deeply double-edge notched (DDEN-T) specimens. Results suggested that the essential work of fracture (w e ) is a material parameter, whereas the non-essential or plastic work ( βw p , where β is the shape factor of the plastic zone) depends on the testing conditions. Various approaches were used to assess w p either explicitly (uniaxial tensile and trouser tests) or via estimation of β [by infra-red thermography (IT)]. IT seemed to be the most reliable technique for this purpose. IT also answered the question whether necking precedes crack growth or these processes occur simultaneously during specimen loading. The out-of-plane type deformation (mode III) in the trouser test resulted in markedly lower w e and higher w p values than those determined by in-plane (mode I) tests on DDEN-T specimens. The difference was attributed to the microstructure-related anisotropy of the PET film caused by biaxial drawing.

Scalable Load Balancing Strategies for Parallel A* Algorithms

In this paper, we develop load balancing strategies for scalable high-performance parallel A* algorithms suitable for distributed-memory machines. In parallel A* search, inefficiencies such as processor starvation and search of nonessential spaces (search spaces not explored by the sequential algorithm) grow with the number of processors P used, thus restricting its scalability. To alleviate this effect, we propose a novel parallel startup phase and an efficient dynamic load balancing strategy called the quality equalizing (QE) strategy. Our new parallel startup scheme executes optimally in Θ(log P) time and, in addition, achieves good initial load balance. The QE strategy prossess certain unique quantitative and qualitative load balancing properties that enable it to significantly reduce starvation and nonessential work. Consequently, we obtain a highly scalable parallel A* algorithm with an almost-linear speedup. The startup and load balancing schemes were employed in parallel A* algorithms to solve the Traveling Salesman Problem on an nCUBE2 hypercube multicomputer. The QE strategy yields average speedup improvements of about 20-185% and 15-120% at low and intermediate work densities (the ratio of the problem size to P), respectively, over three well-known load balancing methods-the round-robin (RR), the random communication (RC), and the neighborhood averaging (NA) strategies. The average speedup observed on 1024 processors is about 985, representing a very high efficiency of 0.96. Finally, we analyze and empirically evaluate the scalability of parallel A* algorithms in terms of the isoefficiency metric. Our analysis gives (1) a Θ( P log P) lower bound on the isoefficiency function of any parallel A* algorithm, and (2) a general expression for the upper bound on the isoefficiency function of our parallel A* algorithm using the QE strategy on any topology-for the hypercube and 2- D mesh architectures the upper bounds on the isoefficiency function are found to be Θ( P log 2 P) and Θ( P[formula]), respectively. Experimental results validate our analysis, and also show that parallel A* search has better scalability using the QE load balancing strategy than using the RR, RC, or NA strategies.

Impact fracture characterization of polymer with ductile behavior

The characterization of ductile polymers with ductile fracture behavior is still a controversial subject. Presently, two approaches based on fracture mechanics have been proposed for the evaluation of impact failure of plastics, i.e., the method using the concept of essential fracture work, and the crack initiation and propagation approach. This paper discusses the validity of the fracture parameters used in these approaches. Additional experimental results and evidence are presented; they indicate that the concept of essential work of fracture cannot be used to characterize the fracture property of plastics. At high loading rates, the fracture energy of plastics can decrease with crack extension, resulting in a variable essential work of fracture. It is also found that the work dissipated in the outer plastic zone as formulated in the concept does not only reflect the non-essential work but is also related to the fracture process. Instead, the approach based on two material parameters should be used to evaluate the impact fracture behavior. Crack initiation and propagation energies should be considered to account for the variation of material's fracture behavior during crack propagation so as to include time rate and size scale effects.

Plane-stress fracture of polycarbonate films

The use of the specific essential work of fracture, W e, to characterize fracture of polycarbonate films is described. It is shown that the plane-stress specific essential work of fracture for polycarbonate film can be obtained from single-edge-notched-tension specimens, by extrapolating the straight-line relationship between the total work of fracture, W f, and ligament length, L, to zero ligament length. From the data, it seems that, for a given film thickness, W e is almost independent of the specimen width but increases with increasing thickness. The non-essential work of fracture as obtained from the slope of a W f versus L plot showed no significant width dependence, and for the majority of thicknesses it was almost invariant with thickness, indicating that the shape of the outer plastic zone surrounding the fracture process zone is almost invariant with the dimensions of the test specimen.