Showing papers in "Ndt & E International in 2012"

On the use of absorbing layers to simulate the propagation of elastic waves in unbounded isotropic media using commercially available Finite Element packages

Abstract: Finite Element models for simulating wave propagation and scattering from defects are vital for ultrasonic methods in NDE. This article addresses methods to dramatically enhance computational efficiency by only meshing a local region of the material surrounding the defect; this reduction requires some kind of boundary, or boundary condition, which absorbs, rather than reflects, any waves arriving at the exterior of the modelled domain. A variety of approaches exist and we take two approaches, Perfectly Matched Layers (PML) and Absorbing Regions, selected specifically as they are readily implemented in commercially available Finite Element packages without requiring the source code. We illustrate both bulk and guided waves, and analysis is used to guide the performance, and thus to plan the use, of each of them. Finally, application examples illustrate the gains yielded by absorbing layer methods in terms of reducing both model size and unwanted reflections.

Ambient vibration testing, dynamic identification and model updating of a historic tower

Abstract: The results of an ambient-vibration based investigation conducted on a historical tower in Italy, to update the 3-D finite element model of the building are presented in this work. The main difficulties are related to the extreme in-homogeneity of the building and the presence of an elevator vain that occupies the posterior part of the tower, forcing to locate the accelerometers only on one facade of the building. The assessment procedure include full-scale ambient vibration testing, modal identification from ambient vibration responses using three different identification methods, finite element modeling and dynamic-based identification of the uncertain structural parameters of the model. A very good match between theoretical and experimental modal parameters was reached and the model updating has been performed to identify some structural parameters.

A new technique to detect defect size and depth in composite structures using digital shearography and unconstrained optimization

Abstract: Advanced composite materials are finding increasing application in aerospace, marine and many other industries due to their performance and structural efficiency. Maintenance inspection of these light-weight structures is a relatively new and difficult task for Non-Destructive Testing (NDT), which need robust methods to be applicable in industrial environments. In this paper, a new numerical–experimental procedure to detect size and depth of flat bottom holes in metallic and laminated composite structures by digital shearography (DISH) is proposed. The flaw detection capabilities of DISH have been evaluated by measuring the dynamic response of defects to applied stresses. Vibration dynamic loading is used to reveal flat bottom holes made with different sizes and placed at different depths in CFRP laminates. The shearographic methodology is based on the recognition of the (0 1) resonance mode per defect. A simplified model of thin circular plate, idealized above each flaw position, is used to calculate the natural frequency of vibrating defects. Then, the numerical difference between experimental resonance frequencies and those computationally obtained is minimized using an unconstrained optimization algorithm in order to calculate the defect depth. Considering the simplicity and rapidity of this technique, the laser shearography methodology is evaluated reliable as NDT method.

Fatigue damage evaluation in A36 steel using nonlinear Rayleigh surface waves

Abstract: This research uses nonlinear Rayleigh waves to characterize the damage due to plastic deformation in A36 steel specimens subjected to quasi-static, monotonic tension, and low cycle fatigue. A36 steel is widely used in the civil infrastructure, such as steel bridges, where fatigue damage can lead to a catastrophic failure. Plastic deformation causes the generation of higher order harmonics in an initially monochromatic Rayleigh wave signal, and this measurable change occurs before macroscopic damage such as cracks appear in a specimen. This increase in the acoustic nonlinearity is produced by plasticity-induced microstructure changes, and thus can be taken as a direct measure of damage. Experiments are conducted using a pair of wedge transducers to generate and detect tone burst ultrasonic Rayleigh surface wave signals. The amplitudes of the first and second order harmonics are measured at different propagation distances to obtain the nonlinearity parameter for a given damage state throughout the fatigue life and monotonic loading process in three specimens. The results of the nonlinear ultrasonic measurements show an increase in the measured acoustic nonlinearity, especially in the early stages of fatigue life. In addition, there is a notably close relationship between the measured acoustic nonlinearity and the cumulative plastic deformation. These results demonstrate the feasibility of using nonlinear Rayleigh waves to characterize damage associated with plastic deformation, and this quantitative information can be a useful input for life prediction models.

Characterisation of voids in fibre reinforced composite materials

Abstract: Voids and porosity are critical imperfections in fibre reinforced composite materials. The aim of this study is to assess the comparative accuracy and reliability of conventional and novel void characterisation techniques for analysing voids within carbon fibre reinforced composite (CFRC) laminates. While microscopy and Archimedes density measurements can only give results of limited accuracy and reliability, micro-computed tomography (micro-CT) analysis was found to have no significant inherent errors and is able to characterise the three-dimensional size, shape and distribution of voids in CFRC laminates. The accuracy of micro-CT was also verified by analysing artificial voids of a known size and shape disbursed throughout a CFRC laminate sample.

Ground penetrating radar imaging of water leaks from buried pipes based on back-projection method

Abstract: In this paper, the application of ground penetrating radar (GPR) imaging for detecting the water leaks from buried pipes is examined. Experimental water leakage conditions for a shallowly buried plastic pipe are realized within the laboratory sand and outdoor soil mediums. The successive B-scan GPR measurements of the mediums are performed at various time instants while the water is leaking out of the pipe. The corresponding time-series B-scan images are reconstructed using the back-projection algorithm that we have specifically formulated for the subsurface GPR imaging applications. The signatures of the leak regions are then assessed by both direct interpretation of the resultant images and application of change detection procedures. The obtained results demonstrate the capability of GPR for locating the sources of the leaks accurately.

Evaluation of residual stress in ferromagnetic steels based on residual magnetic field measurements

Abstract: The paper presents a residual stress evaluation method using the gradients of the residual magnetic field (RMF) components. Distributions of the RMF components were measured on the surface of samples with a various degree of plastic strain. The finite element method was used to model residual stress in samples. The impact of residual stress on changes in the residual magnetic field was shown. A very good qualitative correlation was found between places with residual stress and areas with increased values of the gradients of the RMF components. An algorithm was developed and verified for steel T/P24 to make a quantitative evaluation of residual equivalent (von Mises) stress based on the gradients of tangential component dH T , Y /dx and field gradient dH / dx . Directions of further research were formulated, which included the validation of the method and which took into consideration the factors affecting its accuracy. The developed algorithm can be a significant complement to the Metal Magnetic Memory (MMM) method.

Defect characterisation using pulsed eddy current thermography under transmission mode and NDT applications

Abstract: Pulsed eddy current (PEC) thermography has been successfully applied to detect cracks in metal alloy and carbon fibre reinforced plastic (CFRP) in previous works. In these applications, an inductor and infrared camera are on the same side of components, named reflection mode. In this work, the transmission mode, where the inductor and infrared camera are on opposite sides of component is investigated for defect characterisation through the analytical analysis and experimental studies. The studies show that the detection mechanisms for impact and delamination in CFRP are totally different. Carbon structure can be observed on the early stage of heating phase and impact leading to decreasing conductivity can be also detected in heating phase. However, delamination can be characterised using late stage of cooling phase. Combing the detection mechanisms, principal components analysis and independent components analysis, image reconstruction method is used to improve the sensitivity.

Quantitative prediction of residual stress and hardness in case-hardened steel based on the Barkhausen noise measurement

Abstract: The aim of this study is to predict residual stress and hardness of a case-hardened steel samples based on the Barkhausen noise measurements. A data-based approach for building a prediction model proposed in the paper consists of feature generation, feature selection and model identification and validation steps. Features are selected with a simple forward-selection algorithm. A multivariable linear regression models are used in predictions. Throughout the selection and identification procedures a cross-validation is used to guarantee that the results are realistic and hold also for future predictions. The obtained prediction models are validated with an external validation data set. Prediction accuracy of the prediction models is good showing that the proposed modelling scheme can be applied to prediction of material properties.

Mode conversion behavior of SH guided wave in a tapered plate

Abstract: The present study explores mode conversion of shear horizontal (SH) guided wave when it impinges on smooth defects in plates. The fundamental (SH 0 ) and the first higher (SH 1 ) modes were selectively generated by an electromagnetic acoustic transducer in aluminum plates and the propagating modes at various points were detected by a pinducer. The defects had a flat bottom region and tapered edges. Remaining thickness at the bottom defected region was smaller than the so-called cut-off thickness of SH 1 mode. Both modes exhibited unique mode conversion behaviors in tapered edge, which were interpreted with the dispersion relation. Total reflection of SH 1 mode was also observed at a specific condition. Numerical simulation revealed that the continuous wavenumber change in the tapered region and the consequent zero value at cut-off thickness cause this total reflection.

Eddy-current induced thermography—probability of detection study of small fatigue cracks in steel, titanium and nickel-based superalloy

Abstract: Eddy-current induced thermography (induction thermography, hereon referred to as eddytherm) is an active thermographic method which is capable of rapid and non-contacting detection of out-of-plane cracks in electrically conductive parts. In an eddytherm inspection, the part is induction heated; cracks cause localised changes in the induced eddy-current flow and the associated Joule heating is imaged at the surface of the part with an infrared camera. In this study the detectability of fatigue cracks in steel, titanium and Waspaloy is quantified by novel but simple image processing routines which are specifically applicable to eddytherm inspection. The quantitative detection data is then input into a cumulative log-normal probability of detection model to estimate the probability of detecting the fatigue cracks as a function of crack length. a90,95 (i.e., the crack length which can be detected 90% of the time with 95% confidence) is found to be 0.60 mm for steel, 0.78 mm for titanium and 1.50 mm for Waspaloy (a nickel-based superalloy), showing eddytherm to be an extremely sensitive method.

Crack sizing by laser excited thermography

Abstract: Active thermography is a nowadays widely used NDT method making use of thermal material properties for defect detection. Basically, the sample is heated and the resulting surface temperature is recorded by an IR camera. For laser thermography a laser is used to heat the sample locally. The resulting spherical heat flow allows the detection of voids in arbitrary orientation. In this work, a method is presented which is suitable for the quantitative characterization of depth and angle of surface cracks. The main idea is to evaluate the crack-caused asymmetries of the laser's thermal footprint. The heat is introduced at fixed reference positions relative to the crack. In this paper a data analysis procedure is presented which allows the crack depth and angle to be described by only two characteristic scalar parameters. By investigating artificial test specimens with spark eroded notches, the feasibility of this method is validated. Furthermore, the behavior of the characteristic parameters with variations of crack angle, depth and experimental conditions is studied systematically by FEM simulations, showing that these parameters are well behaved.

Monitoring the hydration of cement using highly nonlinear solitary waves

Abstract: In this paper we present a nondestructive evaluation technique based on the propagation of highly nonlinear solitary waves (HNSWs) to monitor the hydration of cement. HNSWs are mechanical waves that can form and travel in highly nonlinear systems, such as one-dimensional chains of contacting spherical particles (i.e., granular crystals). In the present study, we use a granular crystal-based actuator/sensor to observe the solitary waves propagating to and from the mechanical interface between the transducer and a fresh gypsum cement sample. We hypothesize that the reflected HNSWs traveling along the crystal-based transducer are affected by the hydration process of the cement, and we assess the elastic modulus of the specimen in the localized region of the granular crystal contact. To verify the experimental results, we perform numerical simulations based on a simplified finite element model. The elastic properties of the cement specimen measured by the granular crystal transducer are compared with the compressive strength and the elastic modulus measurements obtained from destructive tests, conducted according to the ASTM C109. We observe good agreement between experiments and numerical simulations.

Effect of the presence and size of a real macro-crack on diffuse ultrasound in concrete

Abstract: In civil engineering structures, the first layer of concrete plays a role in terms of water-tightness, and contributes to the protection of metal frames from corrosion by external chemical agents (water, CO2, chlorine etc.). In concrete, a crack is comprised of an external part with a surface opening, and a completely or partially closed part below the surface. The aim of this paper is to identify the contribution of a real macro-crack on the diffuse ultrasound parameters. The methods ability to characterize the open part of the crack is confirmed. The results reveal the influence of the closed part of the crack, with regions in partial contacts, on the diffusion parameters.

Evaluation of freeze–thaw damage in concrete by ultrasonic imaging

Abstract: This work studies the use of ultrasonic imaging as an evaluation tool in concrete subjected to freeze–thaw (F–T) cycles. To evaluate the damage in this deterioration process, ultrasonic velocity and attenuation images have been generated from concrete specimens with and without air-entraining agents. Two parameters have been proposed from these ultrasonic images according to our experimental setup: the non-assessable area proportion (NAAP) and a weighted average velocity in terms of the NAAP. The proposed parameters have been compared with the recommended failure criteria of the ASTM and Rilem standards, which employ ultrasonic contact measurements. The principal advantage of the use of ultrasonic images and the proposed methodology in comparison with the ultrasonic velocity measurements by contact is the possibility of detection of incipient damage caused by accelerated freeze–thaw cycles.

Assessment of wall thinning in insulated ferromagnetic pipes using the time-to-peak of differential pulsed eddy-current testing signals

Abstract: Pulsed eddy current testing (PECT) is a powerful candidate for the detection of wall thinning of insulated ferromagnetic pipes in petrochemical and power generation plants. The main purpose of this study is to find an efficient and easy-to-use signal feature for the assessment of wall thinning. Analytical modeling for a PECT probe over the insulated piping system is performed and its result is verified by experimental test. Two time-related features, the peak value and the time-to-peak, are found in the differential signal obtained by subtracting the test signal from the reference signal. The time-to-peak is superior to the peak value due to its linear variation with wall thickness. Influences of various conditions in practical testing on the PECT signal are investigated. Results show that the time-to-peak is independent of the insulation thickness and the probe lift-off. Robustness of time-to-peak to probe configuration is also validated by employing three probes of different dimensions and structures. To determine the linear range of time-to-peak with amount of wall thinning, differential signals based on different reference thicknesses are examined. Results show that the time-to-peak only keeps linear for the relative wall thinning less than 60%, but still can be effectively used for calibration purpose in periodical in-service inspection of insulated pipeline.

Ultrasound monitoring of setting and hardening process of ultra-high performance cementitious materials

Abstract: A novel specially designed ultrasonic monitoring apparatus (UMA) for in-situ continuous studying of the early age hydration process of cementitious materials was developed. Utilizing UMA, the early microstructure formation process was systematically investigated for ultra-high performance cementitious materials made with various mineral admixtures (fly ash, slag and silica fume), fine and coarse aggregates, different volume fraction of steel fiber (0, 1%, 2% and 3%). The influence of curing temperature (20, 40, 60, 80 and 90 °C) was also studied. The results show that four stages can be clearly identified during the microstructure formation process of ultra-high performance cementitious materials with sand, aggregate or steel fiber: pre-dormant stage, dormant stage, acceleration stage, and deceleration stage, while only the last three stages occur for the one without fillers and reinforcement. Curing temperature, mineral admixtures, fillers and reinforcement addition have great impact on microstructure formation process. Hydration reaction rate is obviously promoted with an increase in curing temperature. Silica fume addition also accelerates the microstructure formation, while the reverse phenomenon is observed when fly ash and slag are incorporated. Steel fiber addition retards the microstructure formation, especially in high volume fraction of fiber.

Experimental and numerical evaluation of electromagnetic acoustic transducer performance on steel materials

Abstract: Electromagnetic Acoustic Transducers (EMATs) are an attractive alternative to standard piezoelectric probes in a number of applications thanks to their contactless nature. EMATs do not require any couplant liquid and are able to generate a wide range of wave-modes; however these positive features are partly counterbalanced by a relatively low signal-to-noise ratio and by the dependence of EMAT performance on the material properties of the test object. A wide variety of steel materials is employed in many industrial applications, so it is important to assess the material-dependent behaviour of EMATs when used in the inspection of different types of steel. Experimental data showing the performance of bulk shear wave EMATs on a wide range of steels is presented, showing the typical range of physical properties encountered in practice. A previously validated Finite Element model, including the main transduction mechanisms, the Lorentz force and magnetostriction, is used to evaluate the experimental data. The main conclusion is that the Lorentz force is the dominant transduction effect, regardless of the magnitude and direction of the bias magnetic field. Differently from magnetostriction, the Lorentz force is not significantly sensitive to the typical range of physical properties of steels, as a consequence the same EMAT sensor can be used on different grades of ferritic steel.

The impact of magnetostriction on the transduction of normal bias field EMATs

Abstract: A very typical and important application of Electromagnetic Acoustic Transducers (EMATs) is the inspection of ferritic steels with normal bias field transducers. In this case, a controversy has arisen in the literature, as some older studies have indicated the Lorentz force as the main transduction mechanism, while more recent research has claimed that magnetostriction can be two order or magnitudes larger than the Lorentz effect. This is not merely an academic issue, as depending on which physical phenomena dominates, the performance of EMATs on different steel grades might significantly vary and the design of the transducer could be optimized accordingly. This paper analyzes in depth two main assumptions made in the more recent studies, highlighting some inconsistencies. A previously experimentally validated Finite Element model, is used to test the controversial assumptions. It is demonstrated that the mechanical boundary conditions were not modelled correctly leading to a gross overestimation of the role of magnetostriction. The main conclusion is that the magnetostriction force is typically not order of magnitudes larger than the Lorentz force; actually the Lorentz force is the larger transduction effect in non-oxidized ferromagnetic steels, and magnetostriction is only a fraction of it.

Non-collinear wave mixing for non-linear ultrasonic detection of physical ageing in PVC

Abstract: This work considers the characterization of linear PVC acoustic properties using a linear ultrasonic measurement technique and the non-collinear ultrasonic wave mixing technique for measurement of the physical ageing state in PVC. The immersion pulse-echo measurements were used to evaluate phase velocity dispersion and attenuation of longitudinal waves in PVC test specimens. The suggested non-collinear ultrasonic wave mixing technique measurement technique was verified on measurements of laboratory and field PVC test specimens. The measurement results confirm that the ultrasonic wave mixing technique is suitable to estimate the physical ageing state of PVC.

Nonlinear acoustic characterization of micro-damaged materials through higher harmonic resonance analysis

Abstract: A method developed for the analysis of nonlinear systems is applied for the first time to non-destructive testing of diverse materials using vibrations and elastic waves. This method allows to extract the vibrational/acoustical responses of the system, at the excitation frequency and importantly, also at higher harmonics, with the help of a nonlinear convolution signal analysis. It is then possible to make use of the robust nonlinear resonance method together with the harmonic generation method in order to analyze the nonlinear elastic resonances of a sample at excitation frequency harmonics. Definitions of the nonlinear hysteretic parameters associated to higher harmonic resonances are provided. The bases of the signal analysis method are also described. A higher sensitivity to the presence of gradual damage compared to the classical nonlinear resonance method is demonstrated experimentally for diverse materials and configurations.

A differential planar eddy currents probe: Fundamentals, modeling and experimental evaluation

Abstract: This paper presents a new eddy current probe specifically designed to inspect imperfections along Friction Stir Welding joints. The proposed probe has a planar design and a differential operation introducing several innovative aspects in eddy currents generation and sensing. The fundamentals on the probe operation are presented and explained in the presence of a metallic part to be inspected with and without defects. A finite element model was used to detail the probe operation and to assess the influence of several operational parameters on the probe response. Finally, the simulations were validated experimentally using a prototype probe produced in printed circuit board and an aluminum alloy block with standard defects produced using electro-discharge machining.

Real-time full matrix capture for ultrasonic non-destructive testing with acceleration of post-processing through graphic hardware

Abstract: Full matrix capture allows for the complete ultrasonic time domain signals for each transmit and receive element of a linear array probe to be retrieved. While it is more common to use full matrix capture to post-process data to allow for electronic steering, focusing and imaging after the initial inspection processes, due to the data-acquisition and performance limitations of the focusing algorithms real-time inspection systems are not yet common place. This paper investigates several algorithm optimisation techniques utilising standard in-expensive PC architecture with parallelisation undertaken by the graphic processing unit. This approach is further combined with several other software engineering optimisation techniques including threaded data-capture, the use of look-up tables and half-matrix implementation to produce a real-world inspection scenario for benchmark and performance analysis. Experimental results are presented indicating that high frame rates inclusive of data-acquisition and image render are achievable with 32 active transmit and receive elements. This approach is shown to offer significant performance advantages with low implementation and development costs.

Time efficient auto-focussing algorithms for ultrasonic inspection of dual-layered media using Full Matrix Capture

Abstract: This paper describesa number ofmethods for calculating the point of incidence at a planarrefractive interface between dual-layered media for ultrasonic applications in the field of non-destructive testing. It is shown how Snell's law may be expressed as a quartic polynomial, and solved using analytical or numerical techniques to find the point of incidence at the refractive interface. An array transducer mounted onto a Perspex wedge is used to generate ultrasonic imagery of a double ‘v’ butt weld in a low carbon steel plate, using the Full Matrix Capture technique. Curve-fitting algorithms are also presented that allowautomated focussingthrough the wedge-plate interface. Finally, a description is given on how algorithms may be adapted to allow auto-focussing through dual media with a non-planar interface.

The effect of complex defect profiles on the reflection of the fundamental torsional mode in pipes

Abstract: The capacity of guided ultrasonic waves to size real corrosion defects remains challenging due to the complexity of the profiles encountered in practice. In the past many studies on the reflection from defects with relatively simple shapes have been done. The purpose of this work is to analyze the effect of complex defect profiles on the reflection coefficient. A study of the reflection of the fundamental torsional mode T (0, 1) from three dimensional (3D) defects in pipes with different shapes has been carried out. Firstly, flat-bottomed defects with different surface profiles have been analyzed, and then the reflection from 3D defects with varying depth profile has been studied. It is revealed that at a given maximum depth of a finite discontinuity, the peak of the reflection coefficient from a defect is linearly dependent on the circumferential extent of the defect, and is independent of its shape. The influence of the depth profile of a real corrosion defect in the axial and circumferential directions on the reflection coefficient has also been studied. The results from these analyses have been used to propose a practical approach to determine the maximum depth of a complex discontinuity from the reflection coefficient behaviour. This method has been applied to real corrosion patches and validated with experiments.

Utilization of Barkhausen noise magnetizing sweeps for case-depth detection from hardened steel

Abstract: One of the current topics of Barkhausen noise method development is its application to case-depth measurements of hardened components. Usually Barkhausen noise (BN) measurements for case-depth determination are based on the difference in the magnetic properties between the hardened case and the soft base material core. The measurement is done using low magnetizing frequencies. This enables deeper penetration of magnetic field to the ferromagnetic samples compared to the conventional high frequency BN measurements, typically used for grinding burn detection. However, due to the eddy current damping, the penetration depth is limited, depending on the material, to certain distance from the surface. To enable case-depth measurements, the Barkhausen noise measuring device was utilized to obtain data from magnetizing voltage sweeps (MVS). The sweeps were analysed and compared to the case-depths determined with conventional means. A series of hardened samples was investigated including induction and carburizing case-hardened samples. All samples were characterized with X-ray diffraction to study the residual stress state of the surface. Finally destructive characterization was used to verify the actual hardening depth of the studied samples. It was noticed that by studying the MVSs it was possible to evaluate the case-depth values more effectively than in earlier studies. The analysis used in this study utilized the slopes of the MVS sweeps. Furthermore, it was noticed that the ratio of the maximum MVS slopes at different frequencies indicating the case-depth values led to good results.

Stimulated infrared thermography applied to help restoring mural paintings

Abstract: In this work, various examples of the use of the stimulated infrared thermography to help restore mural paintings are presented. First, the principles of this technique are expounded. Then, examples of devices used for the study are described. Finally, we show the possibility of in situ detection of detachments in different mural paintings: “Saint Christophe” belonging to the “Campana” collection in the “Louvre”, painted walls in the “Saint Florentin” church in “Bonnet”, painted ceilings in the “Saint-Savin-sur-Gartempe” abbey (classified in the UNESCO world heritage), and the “Cocteau” frescoes in the “Saint Pierre” vault in “Villefranche-sur-Mer”.

Modelling of the response of an ACFM sensor to rail and rail wheel RCF cracks

Abstract: This paper discusses the relationship between ACFM signal and RCF defects in railway rails and wheels using an FEM model developed with COMSOL Multiphysics that has been verified for single and multiple RCF type cracks. The response to semi-elliptical defects of surface length 2 mm to 40 mm, and elliptical ratio 1:1 to 1.75:1, has been simulated and it is shown that the ACFM signal is most sensitive to, and therefore able to accurately size, RCF defects

Emissivity estimation for accurate quantitative thermography

Abstract: In this paper an emissivity measurement method is proposed; it relies on individual calibration functions, and is based on the spectral response of a specific IR sensor. The reflected temperature is kept constant during the test, and its knowledge is not required. Results of measurements on materials commonly used as emissivity references in quantitative thermography are reported. Computer simulations of indoor and outdoor thermographic inspections show the differentiated influence of emissivity and surroundings temperature on the measurement accuracy. Finally experimental results of absolute and differential temperature measurements are discussed.

A novel beam hardening correction method requiring no prior knowledge, incorporated in an iterative reconstruction algorithm

Abstract: This paper presents a novel beam hardening correction algorithm for X-ray computed tomography which can be used in case no information about the beam spectrum or the material properties is available. This correction is applied in an iterative reconstruction algorithm and takes the effect of beam hardening into account during the reconstruction. The beam hardening is modeled and incorporated in the forward projector of the simultaneous algebraic reconstruction technique (SART). The inclusion of the beam hardening correction does not require any additional iterations compared to standard SART. The algorithm is tested on datasets of several samples and significantly reduces the beam hardening artifacts in these datasets.