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  • 1.
    Hammarberg, Samuel
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mechanics of Solid Materials.
    Kajberg, Jörgen
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mechanics of Solid Materials.
    Jonsén, Pär
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mechanics of Solid Materials.
    Modeling of Ultra High Strength Steel Sandwiches with Lightweight Cores2019In: CHS² 2019 - 7th International Conference on Hot Sheet Metal Forming of High Performance Steel / [ed] Mats Oldenburg, Jens Hardell, Daniel Casellas, 2019, p. 313-320Conference paper (Refereed)
  • 2. Kajberg, Jörgen
    Displacement field measurement using digital speckle photography for characterisation of materials subjected to large deformations and high strain rates2003Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    In many technical processes, material is deformed under conditions involving large deformations (strains) and/or high strain rates. Examples of such processes are collisions, impact, penetration, metal forming, powder compaction and crack propagation. For description of these kinds of situations a variety of constitutive models, based on both physical foundations and empirical considerations, is available. Common for all models is that they contain material parameters, which have to be estimated by utilising experimental methods. For material characterisation under quasi-static conditions standardised tension tests of uniaxially loaded specimens are commonly used. With these tests stress-strain relations are obtained up to moderate strain values, whereupon the onset of strain localisation, so-called necking, restricts their validities. Correction methods have been developed to compensate for the onset of necking (e.g. Bridgman's correction method for round bars). The Taylor impact test and the split Hopkinson bar arrangement are frequently used methods for the investigation of incompressible (volume conserving) materials in the high strain rate regime. Typically, the specimens are short and stubby cylinders, which ideally facilitate a homogeneous state of loading necessary for a simple interpretation of the experimental results. In this thesis a methodology is suggested for characterisation of materials subjected to large deformations and high strain rates, where neither homogeneously loaded specimens nor incompressible behaviour are necessary. Experimental methods similar to standardised tension tests and split Hopkinson bar arrangement are complemented with an optical method, digital speckle photography (DSP), for in-plane point-wise displacement and strain measurements. By using a common digital camera in the former tests and a high-speed camera with a CCD-unit (Charged Coupled Device) in the latter tests digitised images are obtained for the method of DSP. An inverse method is used to estimate the material parameters in constitutive models. Three-dimensional numerical simulations of the specimens are performed by the finite element method (FEM). By adjusting the parameters to give a best fit between experimental and numerical results (displacements and strains) in least-square sense optimal values are obtained. In the quasi-static tension tests true strain values up to 0.8 were obtained for a hot-rolled steel. The mild steel specimens in the high strain rate tests were subjected to strain rates of magnitudes 10^2-10^3 1/s.

  • 3. Kajberg, Jörgen
    High strain-rate experiments using high-speed photography2002Licentiate thesis, comprehensive summary (Other academic)
    Abstract [en]

    In many technical processes, material is deformed under conditions that contain high strain rates. Examples of such processes are collisions, impact, penetration, metal forming and crack propagation. Constitutive models including viscoplasticity have been proposed for these kinds of situations. Common for all models is that they contain material parameters, which are not well known. Experimental techniques like Taylor impact test and split Hopkinson pressure bar have been designed for the investigation of materials subjected to high strain rates. In these methods high strain rates are achieved by subjecting short specimens to rapid loading. For a simple interpretation of experimental results, a homogeneous state of stress and strain is desirable. Short specimens imply high strain rate but if the length and width are similar a nonhomogeneous state of stress and strain will result and the reliability in the evaluated quantities decreases. With the testing techniques mentioned above, it is difficult to use specimens, which are short but slender. In this thesis an experimental method to study material behaviour at high strain rates is developed. In contrast to the classical techniques, this method does not require a homogeneous state of stress and strain. A very small specimen (sub mm) and several larger specimens (up to 5 mm) have been used in the experiments. They are subjected to rapid tensional loading in devices similar to the Hopkinson bar arrangement. For the larger specimens a complete split Hopkinson bar is used, while one of the bars, namely the incident bar, has been omitted when the shorter specimen is tested. The deformation of the specimens is captured with a high-speed camera of image converter type. For the small specimen of sub mm size, the extension of its entire length is evaluated. The estimated strain rate reached well over 10^4 1/s. The larger specimens are evaluated using digital speckle photography (DSP) to give in-plane strain fields. Strains in the domain, 0.01-0.25, are evaluated and strain rates up to 3000 1/s are achieved.

  • 4. Kajberg, Jörgen
    et al.
    Lindkvist, Göran
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mechanics of Solid Materials.
    Characterisation of materials subjected to large strains by inverse modelling based on in-plane displacement fields2004In: International Journal of Solids and Structures, ISSN 0020-7683, E-ISSN 1879-2146, Vol. 41, no 13, p. 3439-3459Article in journal (Refereed)
    Abstract [en]

    A method for characterisation of materials subjected to large strains beyond the levels when plastic instability occurs in standard tension tests is presented. Thin sheets of two types of hot-rolled steel are subjected to tension loading until fracture occurs. The deformation process is captured with a digital camera and by digital speckle photography (DSP) in-plane pointwise displacement fields are obtained. By numerical differentiation and assuming plastic incompressibility the equivalent plastic strain is determined. The characterisation performed in this paper consists of estimating material parameters in two constitutive models. These models are a piecewise linear plasticity model and a parabolic hardening model. By using inverse modelling including finite element analyses (FEA) of the tension tests the material parameters are adjusted to achieve a minimum in a so-called objective function. The objective function is basically a least-square functional based on the difference between the experimental and FE-calculated displacement and strain fields. Due to the large deformations an adaptive meshing technique is used in order to avoid highly distorted elements. The DSP- technique provided measurements, where the uncertainty of the equivalent plastic strain varied between 0.0015 and 0.0056. The maximum obtained strain was approximately 0.8. The true stress-strain curves based on the estimated parameters are validated in the low strain region by comparison with curves from standard tension tests

  • 5. Kajberg, Jörgen
    et al.
    Sjödahl, Mikael
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Fluid and Experimental Mechanics.
    Optical method to study material behaviour at high strain rates2000In: IUTAM Symposium on Field Analysis for Determination of Material Parameters - Experimental and Numerical Aspects: proceedings of the IUTAM Symposium held in Abisko National Park, Kiruna, Sweden, July 31 - August 4, 2000 / [ed] P. Ståhle, Dordrecht: Encyclopedia of Global Archaeology/Springer Verlag, 2000, p. 37-49Conference paper (Refereed)
  • 6.
    Kajberg, Jörgen
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mechanics of Solid Materials.
    Sundin, Karl-Gustaf
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mechanics of Solid Materials.
    High-Temperature Split-Hopkinson Pressure Bar with a Momentum Trap for Obtaining Flow Stress Behaviour and Dynamic Recrystallisation2014In: Strain, ISSN 0039-2103, E-ISSN 1475-1305, Vol. 50, no 6, p. 547-554Article in journal (Refereed)
    Abstract [en]

    In hot forming processes at elevated temperatures like wire rolling, microstructural changes such as repeated dynamic recrystallisation and grain growth occur. An experimental method to obtain the flow stress behaviour and to capture the recrystallised microstructure for materials subjected to large deformations, high temperatures between 900 and 1200 °C and high strain rates around 5000 s− 1 is presented. The method is based on the split-Hopkinson pressure bar arrangement complemented with an inductive heat source. Furthermore, a momentum trap is added to ensure that the specimen is loaded only once. By quenching the specimen directly after the single loading, the dynamically recrystallised microstructure is preserved. The quenching is performed within 0.1 s of loading by dropping the specimen into a water bath. By applying the momentum trap technique, the compressive loading of the specimen could be interrupted at a strain level slightly above the strain level corresponding to the peak stress, which is a good estimation for the onset of dynamic recrystallisation.

  • 7.
    Kajberg, Jörgen
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics.
    Sundin, Karl-Gustaf
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mechanics of Solid Materials.
    Material characterisation using high-temperature Split Hopkinson pressure bar2013In: Journal of Materials Processing Technology, ISSN 0924-0136, E-ISSN 1873-4774, Vol. 213, no 4, p. 522-531Article in journal (Refereed)
    Abstract [en]

    In order to characterise the mechanical response of materials in manufacturing processes, such as wire and bar rolling involving very high strain rates, temperatures and level of straining, an experimental device is presented. The device is suitable for testing at strain rates up to approximately 4000 s−1, temperatures up to 1200 °C (≈1500 K) and strains around 0.5. It is based on the classical split Hopkinson pressure bar and is complemented with an inductive heating source for achieving requested temperatures. By keeping the specimen separated from the Hopkinson bars just until an instant before impact (50 ms) considerable cooling and temperature gradients in the specimen are avoided. Three steel grades, two stainless steels and a high-speed steel, were tested. Four different material models whose parameters were fitted to the obtained experimental data were used for mechanical characterisation: two empirically based and two physically based. Overall, one of the physically based models showed the best agreement between experimental results and the predicted flow stresses.

  • 8. Kajberg, Jörgen
    et al.
    Sundin, Karl-Gustaf
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mechanics of Solid Materials.
    Melin, L.Gunnar
    Luleå tekniska universitet.
    Ståhle, Per
    Luleå tekniska universitet.
    High strain-rate tensile testing and viscoplastic parameter identification using microscopic high-speed photography2004In: International journal of plasticity, ISSN 0749-6419, E-ISSN 1879-2154, Vol. 20, no 4-5, p. 561-575Article in journal (Refereed)
    Abstract [en]

    A combined experimental/numerical method for determination of constitutive parameters in high strain-rate material models is presented. Impact loading, using moderate projectile velocities in combination with small specimens (sub mm) facilitate tensional strain rates in the order of 104-105 s-1. Loading force is measured from one-dimensional wave propagation in a rod using strain gauges and deformation is monitored with a high-speed camera equipped with a microscope lens. A sequence of digital photographs is taken during the impact loading and the plastic deformation history of the specimen is quantified from the photographic record. Estimation of material parameters is performed through so called inverse modelling in which results from repeated FE-simulations are compared with experimental results and a best choice of constitutive parameters is extracted through an iterative optimisation procedure using the simplex method. Results are presented from a preliminary tension test of a mild steel (A533B) at a strain rate well over 104 s-1. The sensitivity of the evaluated material parameters to errors in measured quantities is studied. The method, especially the optical technique for measurement of deformation will be further developed.

  • 9.
    Kajberg, Jörgen
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mechanics of Solid Materials.
    Wikman, Bengt
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mechanics of Solid Materials.
    Viscoplastic parameter estimation by high strain-rate experiments and inverse modelling: speckle measurements and high-speed photography2007In: International Journal of Solids and Structures, ISSN 0020-7683, E-ISSN 1879-2146, Vol. 44, no 1, p. 145-164Article in journal (Refereed)
    Abstract [en]

    A methodology based on inverse modelling for estimating viscoplastic material parameters at high strain-rate conditions is presented. The methodology is demonstrated for a mild steel exposed for compression loading in a split Hopkinson pressure bar arrangement. By using dog-bone shaped specimens nonhomogeneous states of deformation are obtained throughout the entire deformation process. The resulting nonhomogeneous deformation of the specimens is evaluated using digital speckle photography (DSP) to give in-plane point-wise displacement and strain fields. The photographs are captured with a high-speed camera of image converter type, which acquire time resolved images during the impact loading. The experiments are simulated using finite element analysis (FEA), where the material model suggested by Johnson-Cook for high-strain rate conditions are utilised. Experimental and FE-calculated field information are compared in order to estimate the viscoplastic parameter in the Johnson-Cook material model. The estimation is performed by minimising least-square functions that contain the differences in displacements and strains, respectively. The quality of the estimated parameters is studied from statistical point of view.

  • 10.
    Oldenburg, Mats
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mechanics of Solid Materials.
    Sundin, Karl-Gustaf
    Wikman, Bengt
    Kajberg, Jörgen
    Åkerström, Paul
    Material characterisation using advanced experiments and inverse methods2006In: Computational mechanics: Abstracts : abstracts of the papers presented at the regular sessions of the sixth world congress on computational mechanics in conjunction with the second Asian-Pacific congress on computational mechanics, September 5-10, 2004, Beijing, China / [ed] Zhenhan Yao; Mingwu Yuan; Wanxie Zhong, Bejing: Tsinghua University Press, 2006Conference paper (Other academic)
  • 11.
    Sjöberg, Ted
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mechanics of Solid Materials.
    Kajberg, Jörgen
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mechanics of Solid Materials.
    Oldenburg, Mats
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mechanics of Solid Materials.
    Fracture behaviour of Alloy 718 at high strain rates, elevated temperatures, and various stress triaxialities2017In: Engineering Fracture Mechanics, ISSN 0013-7944, E-ISSN 1873-7315, Vol. 178, p. 231-242Article in journal (Refereed)
    Abstract [en]

    A methodology for fracture characterisation at strain rates up to 1000 s−1, temperatures up to 650 °C, and various stress triaxialities is presented. High-speed photography combined with digital image correlation is used to evaluate the strain at fracture. The methodology was successfully demonstrated on aged nickel based Alloy 718, commonly used in the containment structure of aircraft engines. Tensile specimens with four different geometries were loaded to get a wide range of positive stress triaxialities. All specimens originated from one single heat and batch to ensure consistent mechanical properties. The results showed evident stress state dependency on the failure strain, where lower failure strains were observed at higher stress triaxialities for all combinations of temperatures and strain rates. A coupled relationship between the temperature and the stress triaxiality controlling the fracture strain was found. However, any clear dependency on strain rate was hard to detect.

  • 12.
    Sjöberg, Ted
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mechanics of Solid Materials.
    Marth, Stefan
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mechanics of Solid Materials.
    Kajberg, Jörgen
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mechanics of Solid Materials.
    Häggblad, Hans-åke
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mechanics of Solid Materials.
    Experimental characterisation of the evolution of triaxiality stress state for sheet metal materials2017In: European journal of mechanics. A, Solids, ISSN 0997-7538, E-ISSN 1873-7285, Vol. 66, p. 279-286Article in journal (Refereed)
    Abstract [en]

    Sheet metals are often used as safety structures in automotive applications where the fracture behaviour is a key design parameter. Theoretical and experimental observations have shown that the fracture behaviour of many metals depends on the stress state. Modelling the stress state dependency of fracture in Finite Element (FE) simulations has led to the development of advanced stress state dependent fracture criteria. The calibration of advanced fracture models is currently limited by the characterisation methods, which have not developed much during the last decades. Experimental characterisation methods that can determine the stress state accurately are necessary to ensure reliable calibrations of advanced fracture models. In this article, an experimental method to obtain the stress state and its evolution during deformation is presented. The stress state evolution is determined using measured local displacement field data, which were obtained by digital image correlation, coupled with a stepwise modelling method. This article shows that the stepwise modelling method can capture the stress state evolution for three different specimen geometries subjected to tensile loading. The resulting experimentally determined stress state evolutions are compared with the results of FE simulations, and both results are in good agreement. The accurate stress state evolutions characterised directly from experiments using the proposed method enables calibration of advanced fracture models rapidly and reliably

  • 13.
    Sjöberg, Ted
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mechanics of Solid Materials.
    Marth, Stefan
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mechanics of Solid Materials.
    Kajberg, Jörgen
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mechanics of Solid Materials.
    Häggblad, Hans-åke
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mechanics of Solid Materials.
    Experimental Characterization of Triaxiality Stress State Evolution for Sheet Metal MaterialsManuscript (preprint) (Other academic)
  • 14.
    Sjöberg, Ted
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mechanics of Solid Materials.
    Sundin, Karl-Gustaf
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mechanics of Solid Materials.
    Kajberg, Jörgen
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mechanics of Solid Materials.
    Oldenburg, Mats
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mechanics of Solid Materials.
    Reverse ballistic experiment resembling the conditions in turbine blade off event for containment structures2016In: Thin-walled structures, ISSN 0263-8231, E-ISSN 1879-3223, Vol. 107, p. 671-677Article in journal (Refereed)
    Abstract [en]

    An experimental technique has been developed which allows loading of heated sheet material under impact conditions with simultaneous measurement of the impact force history. The combined characteristics of impact loading at elevated temperature makes the experiment ideal for validation of models used to simulate the containment structure surrounding aircraft engines. In this paper experimental results for Alloy 718 are presented, a nickel based super alloy commonly used in hot parts of the containment structure. The experimental results are then compared to simulations in order to validate previously calibrated material parameters. The basic principle of the validation experiment is based on reverse ballistics, in which a thin circular specimen with free boundaries impacts the end of an instrumented rod. Using induction heating the specimen is heated to temperatures up to 650 °C and a gun driven by compressed air accelerates the specimens to desired velocity. In the reported work velocities are kept low enough to avoid cracking and thus the study is limited to plastic conditions, even though the technique is applicable also for fracture studies. The free boundaries of the experiment makes numerical modelling and simulation straightforward, making it valuable as a validation tool. All numerical simulations are performed using the commercial finite element code LS-Dyna and plastic behaviour of the material was modelled with the Johnson-Cook material model

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