A model law for the notch sensitivity of brittle materials

In this paper a model law for the notch sensitivity of brittle materials, for instance hardened cement paste, mortar or concrete is presented. This model law shows that notch sensitivity is a necessary however not a sufficient condition for the applicability of linear elastic fracture mechanics. The model law indicates that notch sensitivity of a brittle material decreases with increasing fracture toughness, decreasing tensile strength and decreasing specimen size. The model law explains the increase of the net failure stress of notched specimens with increasing notch depth after passing through a minimum. Such behavior frequently has been observed in experiments on hardened cement paste, mortar and concrete specimens. Results of flexure tests on notched and unnotched hardened cement paste specimens and concretes of various sizes are in accord with the model law.     

The effect of particles on failure modes of filled polymers

The effect of rigid particles on the fracture mode of polymers that yield with necking was analyzed theoretically with a model of regularly arrayed spherical particles. The adhesion between a polymer and particles was assumed to be weak, and particles were assumed to debond from the polymer before necking. A linear decrease in engineering draw stress with an increase in the filler content was derived. An increase in filler content leads to a transition in deformation mechanism. The transition depends on the ability of the polymer to strain-harden. If the ability to strain-harden is insignificant and the engineering fracture stress (strenght) of the polymer is lower than its yield stress, the transition is from ductile to brittle fracture. If the ability to strain-harden is essential and the strength of the unfilled polymer is higher than its yield stress, the transition (ductile-to-ductile) is from neck propagation to uniform ductile yield. The critical filler contents were determined for both transitions from the properties of an unfilled polymer. The ductile-to-ductile transition without embrittlement is possible if the strength of the unfilled polymer is higher than its yield stress. Results for polymers filled by weakly bonded particles were compared with polymers filled by particles that debond after the yield stress.     

Crack propagation behavior and toughness of V‐notched polyethylene terephthalate injection moldings

The role of the skin and core regions in controlling the effects of V‐notches, on the fracture behavior of PET injection‐moldings, was correlated with their tensile and impact properties. Investigations revealed that there were three distinct fracture behaviors: ductile, semiductile, and brittle fracture transitions. The notch sensitivity factor for strength (K_S) in the ductile and semiductile transitions indicates that the fracture strength was not sensitive to ≤1.5 mm deep notches, which is considered the skin region. The introduction of core‐deep notches (>1.5 mm) resulted in a rapid increase in K_S. On the other hand, the notch sensitivity factor for energy (K_T) shows that the fracture energy was not sensitive at ≤0.5 mm deep notches. However, K_T increased drastically when notches >0.5 mm deep were introduced. The development of an anisotropic skin‐core structure in injection moldings is well acknowledged. This is revealed in a constant fracture behavior between 0.6 and 1.0 mm deep notches. Notably, there was a drastic change in the fracture pattern from ductile to semiductile at a critical 0.6 mm deep notch. The specimens experienced a mixed fracture behavior at 1.5 mm deep notch, which marks a transitional fracture pattern at the interface between the skin and core regions. Lastly, a constant fracture behavior was observed at notch depths ≥1.5 mm. Results show that crack opening, in the samples that had semiductile fracture, was a postnecking phenomenon. Before shear yielding, two shear lines that intersected at 45° were seen to originate from the crack root when a 1.2 kN load was applied. Conversely, crack opening and failure occurred simultaneously in brittle fractures. It is obvious that V‐notches provided a gradual transition in fracture behavior from the skin to the core regions, which confirms that the fracture behavior of PET injection moldings can be dependent on the skin and core structure. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2010     

Notch sensitivity of polymers

The influence of notches on the static tensile strenght, low-cycle fatigue strength, and creep rupture strength was investigated for selected polymeric materials. This investigation was prompted by the unusual phenomena of necking and notch strengthening observed in some glass fiber reinforced plastic materials. Two types of epoxy resin, polymethyl methacrylate and polycarbonate, were studied under static tensile loading. Three sizes of semicircular symmetrical side notch on flat specimens were investigated. It was observed that one of the epoxies was very notch sensitive, while the other exhibited significant (and maximum, out of all the polymers tested) notch strengthening in tensile loading. Perspex and polycarbonate showed a small notch sensitivity for the smallest and intermediate notches but notch strengthening for the biggest notch. The epoxy resin which exhibited notch strengthening was also tested with different percentages of hardener; for the biggest and the intermediate notches, there was a notch strengthening effect and unnotched as well as notched tensile strength showed a peak around 14% hardener. The epoxy which exhibited notch strengthening in tensile loading was next tested in low-cycle fatigue and creep loading. The behavior in low-cycle fatigue and creep loading was remarkably similar: it was found that for this polymer, the notch sensitivity was small in the case of the smallest and intermediate notches, whereas there was a significant notch strengthening effect in the case of the biggest notch. It is recommended that notch-strengthening behavior be added to the other criteria for the selection of matrices for composite materials.     

Mechanical and open hole tensile properties of self‐reinforced PET composites with recycled PET fiber reinforcement

The tensile strength of notched composites is an important factor for composite structural design. However, no literature is available on the notch sensitivity of self‐reinforced polymer composites. In this study, self‐reinforced recycled poly (ethylene terephthalate) (srrPET) composites were produced by film stacking from fabrics composed of double covered uncommingled yarns (DCUY). Composite specimens were subjected to uniaxial tensile, flexural, and Izod impact tests and the related results compared with earlier ones achieved on srPET composites reinforced with nonrecycled technical PET fibers. Effects of open circular holes on the tensile strength of srrPETs were studied at various width‐to‐hole diameter (W/D) ratios of the specimens. In the open hole tensile (OHT) measurements bilinear (yielding followed by post‐yield hardening) stress–strain curves were recorded. The srrPET composites had extremely high yield strength retention (up to 142%) and high breaking strength retention (up to 81%) due to the superior ductile nature of the srrPETs, which induces plastic yielding near the hole thereby reducing the stress concentration effect. The results proved that srrPET composites are tough, ductile notch‐insensitive materials. © 2016 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2016 , 133, 43682.     

Crazing,yielding, and fracture of polymers. I. Ductile brittle transition in polycarbonate

Most thermoplastics far below their glass transition give a brittle fracture when de-formed in uniaxial tension. Bisphenol-A polycarbonates are an exception and deform in a ductile manner. However, it has been observed in Izod impact studies of notched samples that the mode of failure changes from a ductile to a brittle fracture on annealing samples below T_g. It has been found that, when notched samples are stressed, a Griffith type flaw is formed under the notch. The criterion for the ductile brittle transition is evaluated in terms of σG (the stress required to propagate the Griffith flaw), and σ_y, the yield stress for the polymer. It has been found that the density and yield stress for the samples annealed at various temperatures are dependent upon previous thermal history and in particular on the molecular weíAght. On the basis of these measurements, it is concluded that many of the so-called anomalous effects observed with polycarbonate can be explained.     

Precrack hysteresis energy in determining polycarbonate ductile–brittle transition. IV. Effect of strain rate

Effect of deformation rate on the ductile–brittle transition behavior for polycarbonate (PC) with different molar mass, notch radius, and rubber content has been investigated. PC with higher molar mass, notch radius, or rubber-modification possesses a higher critical strain rate when the ductile–brittle transition occurs. Whether a notched specimen will fail in a ductile mode or a brittle mode is already decided before the onset of the crack initiation. If size of the precrack plastic zone exceeds a critical level prior to onset of crack initiation, the crack extension developed later will propagate within the plastic zone and result in a ductile mode fracture. The precrack elastic storage energy, the input energy subtracting the hysteresis energy, is the main driving force to strain the crack tip for crack initiation. The precrack hysteresis energy (directly related to the precrack plasticity) increases with the decrease of the applied strain rate. Therefore, the strain rate is also closely related to the size of the precrack plastic zone. If the strain rate is lower than the critical strain rate, the specimen is able to grow a precrack plastic zone exceeding the critical plastic zone and results in a ductile mode fracture. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 65: 655–665, 1997     

Toughenability of polymers

We demonstrate that all solid polymers are intrinsically brittle and will undergo a ductile to brittle fracture transition based on the nature of their bonding alone. The most effective way of avoiding a ductile to brittle transition is to reduce the plastic resistance to delay reaching the brittle strength which in unoriented polymers is governed by intrinsic cavitation. While a number of possibilities for this exist, the most widely used techniques involve incorporation of rubbery particles that can cavitate or rigid particles that can debond prior to plastic flow. In both approaches the continuous homo-polymer is transformed into a quasi-regular cellular solid that is much more capable of undergoing large local plastic flow by ligament stretching between cavitated particles and is less susceptible to the propagation of brittle cracks under the usual conditions of tensile straining. Under impact conditions, however, in a notched sample which concentrates the strain rate at the notch root, the plastic resistance of the stretching ligaments rises sharply due to two separate but related effects. First, by an increase in the shear modulus due to the high frequency nature of the Izod impact test to fracture, viewed as a quarter cycle oscillation, which directly elevates the flow resistance and second, by the further effect of increase due to the much increased plastic strain rate. At the notch root then, the plastically stretching and strain hardening ligaments are left with a much reduced capacity to strain further before the cavitation stress is reached. While rubber particle-modified polymers can still exhibit considerable toughening, rigid-particle-modified polymers suffer severely from clustering of rigid particles into super critical flaws that trigger brittle response, much like what is encountered in structural steels.Based on their known mechanical response in neat form six, semi-crystalline polymers have been analyzed in detail to evaluate their potential for toughening under impact conditions. The results correlate very well with the experimental findings.     

Strength and Notch Sensitivity of Porous-Matrix Oxide Composites

The effects of matrix strength on the notched and unnotched tensile properties of a family of porous-matrix oxide composites are examined both experimentally and theoretically. Experiments are performed on three composites, distinguished from one another by the amount of binding alumina within the matrix. Increases in alumina concentration produce elevations in unnotched tensile and shear strengths, but the benefits are offset by an increase in notch sensitivity. The degree of notch sensitivity is rationalized on the basis of a model that accounts for interactions between notch tip tensile and shear bands. The model predictions are cast in terms of the ratio of the notch length to a characteristic bridging length scale. These results, in turn, form the basis for a simple analytical formula for notched strength, accounting for effects of elastic anisotropy and finite sample size. The utility of this formula in predicting notched strength is assessed. Issues associated with bridging law shapes and bridging length scales are addressed. The effect of alumina concentration on notch sensitivity is discussed in terms of its influence on the bridging length scale, dictated by the interplay between the unnotched tensile strength, the longitudinal Young's modulus, the degree of in-plane elastic anisotropy, and the fracture energy. The net result is a decreasing bridging length scale and hence increasing notch sensitivity as the matrix is strengthened with alumina.     

聚丙烯材料简支梁缺口冲击性能的时温效应研究

将聚丙烯(PP)树脂在一定注塑工艺条件下制备成用于简支梁冲击测试的样条,分别为ISO注塑A型缺口冲击样条和无缺口样条(然后通过铣缺口机机械加工成A型缺口冲击样条),通过摆锤冲击试验仪进行简支梁缺口冲击强度测试,研究共聚型PP材料注塑缺口和铣缺口冲击性能的时温效应.结果表明,共聚型PP材料铣缺口在标准环境下调节,简支梁缺...     

Fracture and impact properties of polycarbonates and MBS elastomer-modified polycarbonates

Mechanical properties of polycarbonates (PCs) and elastomer-modified polycarbonates with various molecular weights (MW) are investigated. Higher MW PCs show slightly lower density, yield stress, and modulus. The ductile–brittle transition temperature (DBTT) of the notched impact strength decreases with the increase of PC MW and with the increase of elastomer content. The elastomer-modified PC has higher impact strength than does the unmodified counterpart if the failure is in the brittle mode, but has lower impact strength if the failure is in the ductile mode. The critical strain energy release rate (G_c) measured at ?30°C decreases with the decrease of PC MW. The extrapolated zero fracture energy was found at M_n = 6800 or MFR = 135. The G_c of the elastomer-modified PC (MFR = 15, 5% elastomer) is about twice that of thee unmodified one. The presence of elastomer in the PC matrix promotes the plane–strain localized shear yielding to greater extents and thus increases the impact strength and G_c in a typically brittle fracture. Two separate modes, localized and mass shear yielding, work simultaneously in the elastomer-toughening mechanism. The plane–strain localized shear yielding dominates the toughening mechanism at lower temperatures and brittle failure, while the plane–stress mass shear yielding dominates at higher temperatures and ductile failure. For the elastomer-modified PC (10% elastomer), the estimated extension ratio of the yielding zone of the fractured surface is 2 for the ductile failure and 5 for the brittle crack. A criterion for shifting from brittle to ductile failure based on precrack critical plastic-zone volume is proposed.     

Optimization of adhesively-bonded single lap joints by adherend notching

The effect of adherend notching on the strength and deformation behavior of single lap joints was investigated. First, a parametric study was conducted using finite element analysis (FEA). This initial part of the research into the effect of notches on joint behavior involved determination of the optimum notch location and notch dimensions. This was done by using FEA in a series of models with different notch positions and geometries. The results of this parametric study were used to select the most promising lap geometries for further study. Next, more detailed FEA were conducted on the selected lap geometries. These data were compared with the experimental single-lap shear test results to assess the applicability of different failure criteria. Three different model adhesives were used: a rubber toughened film epoxy with nylon carrier, a styrene-butadiene-styrene block copolymer based deformable 'gel' adhesive, and a two-part, metal filled brittle epoxy adhesive. The FEA for single lap joints containing 'top notches' on the unbonded, top side of the adherends, at locations corresponding to the overlap ends, and bonded with the two-part metal filled epoxy provided the best agreement with the experimental results. The experimental results showed a 29% increase in joint strength with the introduction of the notches, which matched very well with the 27% decrease in the peak peel stress observed by the FEA results. For this brittle adhesive, the peel stress is almost certainly the governing failure stress. This was confirmed by matching of the FEA peak peel stress ratios with the experimental load ratios, for both the notched and unnotched specimens.     

Experimental investigation and numerical prediction of static strength and fracture behaviour of notched epoxy-based structural adhesives

The influence of stress concentrations on the tensile static strength and fracture behaviour of notched bulk specimens was investigated by comparing the response of two epoxy-based structural adhesives (a rubber-toughened and a polyurethane-toughened). Numerical predictions of failure stress were carried out using a 3D-FEA model with a hydrostatic dependent elastoplastic material behaviour and the equivalent plastic strain for failure assessment. The ductile adhesive, which plastically deforms more under high stresses, provided experimental evidence of a notch strengthening effect. Conversely, the less ductile adhesive has shown a reduction in tensile strength compared to un-notched samples. For both adhesives fracture surface analysis showed the presence of stress whitening and voids close to the notch regions. These regions could be correlated to higher values of stress triaxiality using numerical simulation. The more ductile adhesive underwent widespread stress whitening prior to failure, whereas the response of the less ductile adhesive was more localised. Numerically based predictions showed excellent agreement with experimental results with average error of 5.1% for different notch types in both adhesives.     

An experimental examination of fracture criteria using brittle polystyrene

A four-point bend test was performed on injection-molded bar-shaped polystyrene specimens with notches of varying depths. The material investigated was found to be linear elastic and brittle. From the load–displacement curves, various fracture toughness parameters based on energy release rate theories and stress–intensity factors were calculated. The stress concentrations arising from the presence of finite size notches with finite root radii were also calculated. The local stress at crack initiation was found to be nearly constant for all specimens investigated while the fracture toughness parameters based on energy release rates were not constant. A distinct change in the crack propagation behavior was observed when the curvature of the stiffness vs. notch depth curve changed sign, clearly defining the onset of unstable crack growth.     

Notch sensitivity of polycarbonate and toughened polycarbonate

Notch sensitivity, the effect of a notch radius on the impact behavior of polycarbonate and rubber‐toughened polycarbonate, is investigated by using a model based on the slip‐lines field theory. Impact strength, determined by the Charpy impact test, was found to increase drastically with an increasing notch radius for pure polycarbonate, whereas the increase of impact strength with increased notch radius was not as extreme for rubber‐toughened polycarbonate. These results indicate that the inclusion of rubber particles reduces notch sensitivity. An examination of fracture surfaces reveals that cracks were initiated by internal crazing at some distance from the notch tip for specimens with blunt notches. For pure polycarbonate, the impact strength is found to have a linear relationship with the square of the notch radius, which is in good agreement with that predicted by the proposed model. However, for rubber‐toughened polycarbonate, the linear relationship broke down as the notch radius increased due to the enhanced toughening effect. The proposed model can be applied to clearly explain the notch sensitivity of ductile polymers which exhibit large plastic yielding around the notch tip. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 89: 3115–3121, 2003     

Ductile tearing instability in some engineering thermoplastic blends

The stability of ductile crack growth in two engineering thermoplastic blends is examined. The blends are a poly(phenylene oxide)/nylon 6,6 blend and a poly(butylene terephthalate)/polycarbonate blend. Fracture tests were performed with single-edge notched specimens in tension and three-point bending over a wide range of test speeds. Both larger radius notches and longer specimens were found to promote ductile tearing instability. This behavior is attributed to the higher driving force for crack growth produced by increased elastic energy storage before crack initiation. Over a certain range of test speeds, these factors lead to a novel effect of notch sharpness on toughness; a sharp notch gives rise to a higher fracture energy than does a blunt notch. The results are discussed in terms of the tearing modulus concept developed by Paris and co-workers.     

Fracture behavior of polypropylene/ ethylene- diene-terpolymer blends : Effect of temperatures,notch radius and rubber content

The mechanical fracture and ductile-brittle transition (DBT) behavior, hysteresis phenomenon and the plastic zone size of polypropylene (PP) / ethylene-propylene-diene terpolymer (PP/EPDM) blends were investigated by varying EPDM content and notch radius under different temperatures. An increase in test temperature or rubber content in the PP/EPDM blend results in lower yield stress and Young's modulus. The ductile-brittle transition temperature (DBTT) of the notched impact strength decreases with the increase of the EPDM content. However, the DBTT is fairly independent of the notch radius. SEM morphologies of the fracture surfaces indicate that two separate modes, localized and mass shear yielding, work simultaneously in these blends. The plane-strain localized shear yielding dominates the brittle failure at lower temperatures, whereas the plane stress mass shear yielding dominates the ductile fracture at higher temperatures. The presence of EPDM rubber decreases the yield stress of the PP/EPDM blend due to the overlapping stress fields of adjacent particles, resulting in higher hysteresis energy. The relationships among the test temperature, hysteresis loss energy and the size of plastic zone are discussed in detail.     

Surface embrittlement of ductile polymers: A fracture mechanics analysis

The embrittlement of ductile polymers resulting from outdoor weathering or aging or from the application of brittle surface coatings is explained using fracture mechanics principles. It is shown that in order for surface embrittlement to occur, the brittle surface should have a dynamic stress intensity factor at the brittle/ductile interface that exceeds the arrest toughness of the ductile polymer. This phenomenon is modeled using duplex tensile specimens fabricated from poly(methylmethacrylate) (brittle layer) and polycarbonate (ductile substrate) as well as from styrene-acrylonitrile and acrylonitrile-butadiene-styrene copolymers.