In this work, the essential work of fracture (EWF) method is introduced for a peridynamic (PD) material model to characterize fracture toughness of ductile materials. First, an analytical derivation for the path-independence of the PD J-integral is provided. Thereafter, the classical J-integral and PD J-integral are computed on a number of analytical crack problems, for subsequent investigation on how it performs under large scale yielding of thin sheets. To represent a highly nonlinear elastic behavior, a new adaptive bond stiffness calibration and a modified bond-damage model with gradual softening are proposed. The model is employed for two different materials: a lower-ductility bainitic-martensitic steel and a higher-ductility bainitic steel. Up to the start of the softening phase, the PD model recovers the experimentally obtained stress-strain response of both materials. Due to the high failure sensitivity on the presence of defects for the lower-ductility material, the PD model could not recover the experimentally obtained EWF values. For the higher-ductility bainitic material, the PD model was able to match very well the experimentally obtained EWF values. Moreover, the J-integral value obtained from the PD model, at the absolute maximum specimen load, matched the corresponding EWF value.

In peridynamics, boundary effects generally appear due to nonlocality of interparticle forces; in particular, end effects are found in 1D bars. In a previous work by Eriksson and Stenström (J Peridyn Nonlocal Model 2(2):205–228, 2020), a simple method to remove end effects in certain types of 1D bars, or to homogenize such bars, was presented for bars with constant micromodulus. In this work, which is a continuation of Eriksson and Stenström (J Peridyn Nonlocal Model 2(2):205–228, 2020), the homogenizing procedure is applied to bars with a linear, or “triangular,” micromodulus. For the examples studied, common in practice, the linear elastic behavior of a homogenized bar, is identical to that of a corresponding classical continuum mechanics bar, independently of the interparticle force range and total number of material points of the bar.

The J-integral is in its original formulation expressed as a contour integral. The contour formulation was, however, found cumbersome early on to apply in the finite element analysis, for which method the more directly applicable J-area integral formulation was later developed. In a previous study, we expressed the J-contour integral as a function of displacements only, to make the integral directly applicable in peridynamics (Stenström and Eriksson in Int J Fract 216:173–183, 2019). In this article we extend the work to include the J-area integral by deriving it as a function of displacements only, to obtain the alternative method of calculating the J-integral in peridynamics as well. The properties of the area formulation are then compared with those of the contour formulation, using an exact analytical solution for an infinite plate with a central crack in Mode I loading. The results show that the J-area integral is less sensitive to local disturbances compared to the contour counterpart. However, peridynamic implementation is straightforward and of similar scope for both formulations. In addition, discretization, effects of boundaries, both crack surfaces and other boundaries, and integration contour corners in peridynamics are considered.

Because of the nonlocal interparticle forces inherent in peridynamics, surface, boundary, and end effects appear in 3D, 2D and 1D body problems, respectively. In certain situations, the effect is seen as a disturbance, and various efforts, mostly centering on 2D and 1D problems, have been made to reduce it. A simple method has been derived to remove the end effects in a 1D body by homogenizing the body. When a certain body type, common in practice, is homogenized, its linear elastic behavior, independent of the interparticle force range and with a finite number of material points, in the limit infinite, is identical to that of a corresponding classical continuum mechanics body.

Peridynamics is a nonlocal formulation of solid mechanics capable of unguided modelling of crack initiation, propagation and fracture. Peridynamics is based upon integral equations, thereby avoiding spatial derivatives, which are not defined at discontinuities, such as crack surfaces. Rice’s J-contour integral is a firmly established expression in classic continuum solid mechanics, used as a fracture characterizing parameter for both linear and nonlinear elastic materials. A corresponding nonlocal J-integral has previously been derived for peridynamic modelling, which is based on the calculation of a set of displacement derivatives and force interactions associated with the contour of the integral. In this paper, we present an alternative calculation of the classical linear elastic J-integral for use in peridynamics, by writing Rice’s J-integral as a function entirely of displacement derivatives. The accuracy of the proposed J-integral on displacement formulation is investigated by applying it to the exact analytical displacement solution of an infinite specimen with a central crack and comparing the exact analytical expression of its J-integral. Further comparison with a well-known peridynamic crack problem shows very good agreement. The suggested method is computationally efficient and further allows testing of the accuracy of a peridynamic model as such.

Previous preliminary testing within the European R&D project PROLIFE, (RFCS 2015-00025) of bolted lap joints loaded in shear has confirmed that small hard indenters inserted into a joint may indeed increase the effective friction of the joint. In order to further explore this feature, additional tests have been carried out with plates of different surface treatment and indenter size. Plates of structural steel grade S355+N were used in the experiments. Some plates were treated with fine blasting and others with a rougher treatment. Most plates were treated in the same way as steel components in new steel bridges in Sweden. For tests with the AMA surface treatment, 2.5 and 5.0 mm diameter stainless steel spherical indenters and 3.0 mm diameter silicon nitride spherical indenters were used. The necessary pre-loads to fully impress a 2.5 or a 5.0 mm stainless steel indenter into a steel plate surface are 10.6 and 41.0 kN, respectively, and for a 3.0 mm silicon nitride indenter 17.7 kN. In the lap joint tests an M24 bolt with a pre-loading force of 240 kN were used and the number of indenters adopted accordingly. The results were compared with each other and to slip factors according to Eurocode. The results confirm certain Eurocode friction coefficients and they further indicate which parameters need further research, in order to develop more efficient bolted friction lap joints.

Indenters in the slip planes of a bolted lap joint increase its load bearing capacity. In an experimental study, conducted at the Luleå University of Technology, Sweden, a part of the European R&D project PROLIFE, RFCS 2015-00025, indenters between two plates a) were loaded in compression and b) shear loaded in a lap joint. The load to press a 2.5 mm diameter stainless steel indenter 2.3 mm into the plates was 11 kN and the effective friction of the joint was improved. In a reference test with two shear planes and plain as rolled plates, no indenters and an M30 bolt pre-loaded to 320 kN, the joint slip resistance force was 54.5 kN and the effective friction coefficient μeff=0.09. For an identical arrangement but with 29 indenters per shear plane, the slip resistance was close to 250 kN and μeff was increased to 0.40, at the current Eurocode acceptable joint slip of 0.15 mm.

In this work, the finite element method is employed to gain an understanding of the behaviour of a cracked bridge roller bearing in service. The cracked roller is considered as an edge-cracked disk (two-dimensional plane strain system) subjected to a radial compressive line load. The crack parameters K_I and K_II are calculated for the relevant load configuration and angle of disk rotation. The calculated data are also used to check the accuracy of approximate SIF solutions reported earlier [1] and [2]. For plain Mode I loading very good agreement is found between the obtained results and data presented in Schindler and Morf (1994). 

The paper is aimed at finding the likely failure mechanism of a bridge roller bearing made of high strength martensitic stainless steel. Spectroscopy and finite element stress analysis of the roller indicated that an initial radial surface crack, found at an end face of the roller and close to the contact region, was induced by stress corrosion cracking (SCC). The initial crack subsequently changed shape and increased in size under growth through fatigue and finally formed a quarter-circle radial crack centred on the end face corner of the roller. Numerically computed stress intensity factors for the final crack showed that crack loading was predominantly in Mode II. For a crack size as observed on the fracture surface, the maximum service load, as specified by the manufacturer, enhanced by a certain roller bearing misalignment effect, was sufficient for failure through fracture.

With the innovation of elastomeric bearings in the mid-1950s steel bearings lost their interest and significance both in research and development and subsequently even in application. Steel bearings were gradually abandoned in bridges, followed by the technical literature and design standards. However, a great number of steel bearings remain today in service world-wide and will pose their particular challenges in the future. To the author’s knowledge, just in Sweden, high strength stainless steel bearings still exist in no less than some 650 bridges. In recent years, a large number of such bearings have failed with an alarmingly high frequency in Sweden during a period of six to twenty years after installation making them a serious maintenance cost issue.

After a brief summary of the history of high strength stainless steel bearings, the paper reviews service experience of such bearings in Sweden and elsewhere. Accompanying finite element analyses were performed in order to gain insight into the likely failure mechanism. Finally, this comprehensive review leads to a conclusion that identifies the causes of the failures occurred and makes some recommendations.

Although previous investigations of the stainless steel bearings have not been able to clearly identify the cause(s) of the failures occurred, it is found that the failures primarily occurred due to initiation of cracks through stress corrosion cracking followed by fatigue crack growth requiring a certain stress range and a sufficiently large number of cycles until final failure ensued through sudden and instable fracture after fatigue growth to a critical crack size.