Concept Of Linear Notch Mechanics Research Articles

Effectiveness of Linear Notch Mechanics under the Condition of Small Scale Yielding

The linear notch mechanics (LNM) was proposed by H. Nisitani in 1983. The concept of LNM can assure the occurrence of the same phenomena in a notched specimen and a real object. The effectiveness of LNM under the condition of small scale yielding has not been confirmed sufficiently. In this paper, the effectiveness of LNM under the condition of small scale yielding is discussed based on the results of FEM elastic-plastic analyses.

Evaluation of Fatigue Strength of Arbitrarily Notched Specimens with Small Defects Based on Linear Notch Mechanics.

Fatigue tests are carried out on the notched specimens of forged steels with small defects under rotating bending and it is shown that the fatigue strength of notched specimens having arbitrary sizes of notch radius and notch depth can be predicted systematically based on the concept of linear notch mechanics. The main results are summarized as follows. (1) When the notch radius is larger than a definite size, the fatigue limit is affected and decreased by the existence of defects. This is due to the statistical factor, that is, the difference in sizes of surface areas exposed to the danger of crack initiation. (2) The fatigue limits of plain specimens in the two present materials are smaller than those of some bluntly notched specimens, respectively. (3) The fatigue strength of a bluntly notched specimen having an arbitrary size can be predicted systematically by using a master-curve derived from the concept of linear notch mechanics, including the cases where crack initiations are affected by the existence of defects.

Effect of Pre-strain on Notched Fatigue Strength of 0.45% C Steel.

Rotating bending fatigue tests were carried out on the plain and notched specimens of annealed and pre-strained 0.45% carbon steels. The obtained results are discussed based on the concept of linear notch mechanics. The main results are summarized as follows : (1) Fatigue limit of plain specimen σw0 increases monotonously with the increase in the value of Vickers hardness. (2) The value of notch radius ρ0 at the branch point is almost independent of pre-strain. (3) The notch sensitivity for σw1 and σw2 are almost independent of pre-strain. Therefore, the values of σw1 and σw2 of pre-strained specimens can be predicted through the value of σw0 of pre-strained specimens and the relations between of K1σw1-1/ρ and K1σw2-1/ρ of annealed specimens.

Damage of Notched FRP Plates under Static Loads. Evaluation of Damage using Luminance Measuring System.

The validity of the concept of linear notch mechanics for evaluating the damage near the notch root of notched FRP plates is investigated experimentally. An experimental method is presented for examining the effect of notch geometry on the damage near the notch root of FRP plates in tension and bending. Two kinds of FRP plate were used : a woven roving glass fabric/epoxy laminate and a short-glass-fiber reinforced polycarbonate. To evaluate the damage near the notch root, we measured the luminance distributions by means of the luminance measuring technique using a CCD camera. The results show that the growth of the damaged zone near the notch root was governed predominantly by both the notch-root radius and the maximum elastic stress at the notch root, while it was independent of notch depth and type of loading. Using linear notch mechanics, the experimental results can be clearly explained.

切欠きをもつＦＲＰ板の静的破壊特性に及ぼす切欠形状と繊維方向の影響

A fracture criterion based on the concept of linear notch mechanics for predicting strength in static load is subjected to further theoretical and experimental scrutiny. An experimental program is presented which examines the effects of notch-root radius and fiber orientation on the fracture behavior of FRP plates. This is accomplished by obtaining experimental data in tension and bending tests on a glass cloth/epoxy laminate (JIS: EL-GEM) containing notches with a wide range of notch-root radii. To examine the effect of fiber orientation on the fracture behavior, the stress distributions near the notch root of notched FRP plates were determined by finite element analysis. The experiment showed that the nominal stress at fracture decreased with decreasing notch-root radius for a constant notch depth. It has been verified that the maximum elastic stress at the notch root when the specimen fails, σmax, c, is governed by the notch-root radius ρ only and independent of type of static load. In other words, the one-to-one relation curve between σmax, c and ρ for notched FRP plates in tension tests agrees well with the curve in bending tests. The fracture characteristics mentioned above was independent of fiber orientation. On the basis of the concept of linear notch mechanics, the experimental results can be clearly explained.

Effect of Notch Depth on the Fatigue Damage of Notched FRP Plates.

A fatigue failure criterion based on the concept of linear notch mechanics for predicting the fatigue life of notched FRP plates is subjected to further experimental scrutiny. An experimental program is presented which examines the effect of notch depth on the fatigue failure of notched FRP plates. This is accomplished by obtaining experimental data on the notched specimens of a glass fabric/epoxy laminate for a wide range of notch geometries in pulsating tension. The process of initiation and growth of fatigue damage near the notch root was measured by means of the luminance-measuring system with a CCD camera. The experiment shows that the number of cycles required to initiate fatigue damage was governed predominantly by both the notch-root radius and the maximum elastic stress at the notch root, while it was independent of notch depth. On the basis of the fatigue failure criterion mentioned above, the experimental results can be clearly elucidated.

ガラス繊維強化ポリカーボネート切欠平板の静的破壊特性

A fracture criterion based on the concept of linear notch mechanics (LNM) for predicting the failure load of composites containing stress concentrations is subjected to further experimental scrutinization. An experimental program is presented which examines the effect of notch geometry on the fracture of FRP plates. This is accomplished by obtaining experimental data on tension tests and fourpoint bending tests of short-glass-fiber reinforced polycarbonate plates having U-shape notches for a wide range of notch-root radii and depths. The concept of LNM is based on the similarity of the severity near the notch root. The severity near the notch root can be expressed by both the maximum elastic stress σmax and the notch-root radius ρ. On the basis of the concept of LNM the fracture criterion for notched plates is expressed as: σmax=σmax, c(ρ), where σmax, c is the material constant, which is governed by the notch-root radius ρ only and independent of notch geometry and specimen size. The experimental results can be clearly explained on the basis of the concept of LNM, and show that the fracture criterion for notched plates mentioned above is applicable to the material used.

ＦＲＰ切欠試験片の疲労損傷に及ぼす切欠半径の影響

Fatigue tests under plane bending and pulsating tension were carried out the notched FRP plates for a wide range of notch-root radii and stress amplitudes. An attention was focussed on the fatigue damage development near the notch root of specimens. The luminance at the limited spot near the notch root was measured successively during fatigue tests to evaluate the fatigue damage. Closer observation by means of a scanning electron microscope revealed that the initiation of microcracks at the notch root was accompanied with a decrease in luminance near the notch root. The experiment shows that the number of cycles to fatigue damage initiation is determined by both the maximum elastic stress at the notch root and the notch-root radius. On the basis of the concept of linear notch mechanics, the experimental results can be clearly elucidated and a criterion of fatigue damage initiation is determined in terms of a combination of the maximum elastic stress, σmax, notch-root radius ρ and the number of cycles to fatigue damage initiation Nd. The criterion is expressed as: σmax·(Nd)m=C(ρ), where m is the material constant. The parameter C is the material constant, which is governed by the notch-root radius only and is independent of other notch geometries and specimen size. By applying the criterion derived here, it is possible to make an accurate estimate of the fatigue life for notched FRP plates.

Fracture of FRP plates containing notches or a circular hole under tension

A fracture criteria based on the concept of linear-notch mechanics (LNM) for predicting the tensile strength of composite laminates containing stress concentrations is subjected to further experimental scrutinization. An experimental program is presented which examines the effect of notch-root radius and the hole-size effect on the fracture of the FRP plates. This is accomplished by obtaining experimental data on a glass-fiber/epoxy laminate containing notches or through-the-thickness circular holes for a wide range of sizes. The experiment shows that the maximum elastic stress at the notch root or at the edge of the hole when the specimen fails is governed by the notch-root radius or the hole size. On the basis of the concept of LNM, the experimental results can be clearly explained, and the limiting condition for the fracture of FRP plates containing notches or a circular hole is determined.

Fracture of FRP plates containing a circular hole under tension.

A fracture criterion developed previously for predicting the uniaxial tensile strength of composite laminates containing notches is subjected to further experimental scrutinization. An experimental program is presented which examines the hole size effect in fractures of FRP plates. This is accomplished by obtaining experimental data on glass cloth-epoxy laminates containing through-the-thickness circular holes for a wide range of hole and specimen sizes. In the case that the ratio of hole size to the specimen width is less than 0.25, the maximum elastic stress at the edge of a hole when a specimen fails is governed by the hole size alone, and is independent of specimen width. On the basis of the concept of linear notch mechanics, the experimental results mentioned above can be clearly explained, and the limiting condition for the fracture of FRP plates containing a circular hole is expressed. The condition is the same as what is exprssed in the case of FRP plates containing notches.

Fracture Criterion of Notched Plates of FRP

The influence of notches on the static tensile strength of plates was studied for a composite material. Tension tests on notched plates made of fiber glass/epoxy laminates have been carried out for a wide range of notch root radii. All notched specimens failed in a brittle manner through the formation of a small deformation near the notch root. This experiment shows that the nominal stress at failure decreases with decreasing notch root radius, and it approaches a constant value when the notch root radius is less than about 0.2 mm. It has been verified that the maximum elastic stress at the notch root when the specimen fails is governed by the notch root radius alone and is independent of notch depth. On the basis of the concept of linear notch mechanics, the experimental results mentioned above can be clearly explained, and the limiting condition for the fracture of notched plates of composite materials is determined. This condition is the same as that of notched engineering plastics.

円周切欠きをもつ熱可塑性プラスチック丸棒の引張りにおける破壊の条件

The influence of notches on the static tensile strength was studied for selected polymeric materials. The tension tests on the grooved shafts have been carried out for a wide range of notch tip radii and depths. The materials used were the following seven kinds of thermoplastics; PC, PVC, PMMA, ABS, Nylon 66, PP and PE. The sharply notched specimens failed in a brittle manner and the bluntly notched specimens failed in a ductile manner for all the materials except PMMA. All the notched specimens of PMMA failed in a brittle manner. The predominant factor for determining the brittle-ductile transition of the fracture mode was the notch tip radius. The experimental results were discussed in terms of a relation between the maximum elastic stress at the notch tip, σmax, and the notch tip radius. In the case of brittle fracture, it has been verified that the σmax at which the specimen failed is governed by the notch tip radius alone and is independent of notch depth for all the specimens. On the basis of the concept of linear notch mechanics, the experimental results mentioned above could be clearly explained and the limiting condition for fracture of the grooved shafts of rigid plastics was expressed. The condition is applicable commonly to seven kinds of thermoplastics.

Fracture criterion of notched plates of FRP.

The influence of notches on static tensile strength was studied for a composite material. Tension tests of notched plate for glass cloth/epoxy laminates have been carried out for a wide range of notch tip radii. All notched specimens failed in a brittle manner through the formation of small deformation near the notch tip. The experiment shows that the nominal stress at failure decreases with decreasing notch tip radius and it approaches a constant value when the notch tip radius is less than about 0.2mm. It has been verified that the maximum elastic stress at the notch tip when the specimen fails is governed by notch tip radius alone, and is independent of notch depth. On the basis of the concept of linear notch mechanics, the experimental results mentioned above can be clearly explained, and the limiting condition for the fracture of notched plates of composite materials is expressed. The condition is the as same as what is expressed in the case of a notched solid polymer.

Tensile fracture criterion of high strength steel specimens with a circumferential notch.

Tensile tests of a high strength steel were made on specimens having a circumferential notch. The values of the notch root radius and notch depth were varied over a side range. All the data were examined based on the concept of linear notch mechanics. For the present material, it is considered that the load for the static tensile fracture of structures can be estimated approximately by linear notch mechanics.

Damage Near The Notch Root Of Notched FRP PlatesIn Static Load - Evaluation Of Damage By ALuminance-measuring System

The validity of the concept of linear notch mechanics for evaluating the damage near the notch root of notched FRP plates is subjected to further experimental scrutiny. An experimental program is presented which examines the effect of notch-root radius on the initiation and growth of damage near the notch root of FRP plates in tension and bending. Two kinds of FRP plates were used: a woven roving glass fabrics/epoxy laminate and a short glass fiber reinforced polycarbonate. To evaluate the damage, we measured the luminance distributions by means of the luminance measuring technique with a CCD camera. The experiment shows that the growth of damaged zone near the notch root was governed predominantly by both the notch-root radius and the maximum elastic stress at the notch root, while it was independent of notch depth and type of loading. On the basis of the concept of linear notch mechanics, the experimental results can be clearly elucidated.

Fatigue Strength Of Cast Stainless Steel In NotchedOr Shouldered Specimens

In most cases, the failure or fracture of machines and structures are brought by the stress concentration due to the existence of a crack or a notch. On the other hand, it is well known that the elastic maximum stress is not enough to predict the failure or fracture. Concerning a crack, linear fracture mechanics can play an important role to predict the fracture or yield in the neighborhood of a crack tip. However, concerning a notch, the concept corresponding to the linear fracture mechanics is not discussed fully until now. Originally, linear fracture mechanics should be called as linear crack mechanics. If we call linear fracture mechanics as linear crack mechanics, we will notice easily that linear notch mechanics is necessary. In this paper, it has been shown that the fatigue strength of a notched or a shouldered specimen having an arbitrary size can be predicted systematically by using a master-curve derived from the concept of linear notch mechanics.