Local Heat Treatment Research Articles

Effect of local heat treatment on residual stresses in an in-service repair welded pipeline

Abstract The multi-pass fillet welds of casing pipe were welded onto the in-service pipeline, which is widely used in pipeline repairs. However, the residual stress of repairing welded joints is larger, and it is easy to cause cracks in the heat-affected zone. In this paper, the local heat treatment was used to adjust the residual stress of the repaired welded joint of the in-service pipeline. The results show that the local heat treatment is very useful for reducing the residual stress of the repair welding joint of the in-service pipeline.

Investigation of the Plane Strain Behaviour of a Laser-Heat Treated Aluminium Alloy

The necessity of complex-shaped components characterized by superior mechanical properties and limited weight is moving the attention to the Aluminium (Al) alloys. Deep Drawing Steel grades possess superior stamping characteristics and formability with respect to Al alloys. But the need of light-weighting pushes towards the adoption of materials with optimal strenght-to-weight ratio, like Al alloys. Todays Al alloys are certainly used in the transport sector but their formability (at room temperature) is poorer than Deep Drawing Steel grades, which still hinders their massive implementation in the forming processes and drives the research toward innovative manufacturing solutions. One of the most promising approach to overcome such a limitation and, thus, manufacture complex component using cold forming processes, is the adoption of local heat treatments to obtain a suitable distribution of material properties able to enhance the formability at room temperature.The design of cold forming using locally modified blanks needs: (i) an extensive investigation of the material behaviour at room temperature after the local heating and (ii) the adoption of a Finite Element approach. As for the former aspect, the authors proposed a fast and comprehensive methodology to investigate the hardening behaviour of an Al alloy (AA5754-H32) locally annealed by laser heat treatment. Using a similar approach, the hardening model was then enriched by considering the normal anisotropy, evaluating the correlation between the Lankford parameter and the material condition reached at the end of the local treatment. To improve the knowledge on the plastic response of the material, the present work focusses on the characterization of the plane strain behavior of the AA5754, initially in wrought condition (H32) and subsequently modified by laser heating. In particular, the study proposes a new quasi-homogeneous specimen which combines the local heating profile with an optimized geometry to produce a prevailing plane strain condition in the heat-treated zone. In such a way, data about the material response in the plane strain condition could be obtained for a large range of material conditions determined by the preliminary heat treatment.

Hot Spinning of Cutting Blades for Food Industry

The spinning process is a flexible incremental forming process for the manufacturing of axially-symmetric sheet metal or tubular components with functionally graded properties. It is characterized by the utilization of universal tooling geometries and quite low forming forces. The process has a high potential to reduce material waste, to extend the forming limits and to achieve more complex geometries as well as favorable part properties [1]. Current research work at the Chair of Forming Technology (LUF) is focused on innovative flow-turning processes that have a high potential for producing flat components with excellent geometrical and mechanical properties while keeping process times short [2]. In combination with process-integrated local heat treatment, the new spinning process is predestined for the efficient forming of ultra-high-strength steel or tailored materials. Due to the desired field of food industry only food-safe materials such as special stainless steels are being investigated. This paper presents an innovative machine layout as well as an adequate process design for the production of high-performance circular knives with optimized mechanical hardness. In this context, particular attention is paid to various areas of temperature control as well as process-related challenges during the process.

Effect of Pre-Heating and Post-Weld Local Heat Treatment on the Microstructure and Mechanical Properties of Low-Cost β-Titanium Alloy Welding Joints, Obtained by EBW

Titanium (Ti) is highly valued for its strength-to-weight ratio and corrosion resistance. However, after it is processed to a wrought, or shaped form, it is typically in excess of 40 times more expensive than the corresponding steel part and nearly 20 times more expensive than the aluminum part. The high production costs of titanium in comparison to other structural metals is the main limiting factor for the wide employment of titanium. Cost reduction can be addressed considering creative fabrication methods and/or formulating new chemical compositions. In general, low-cost technology of titanium alloy can be implemented from raw material, alloy design and processing and forming. The core idea of low-cost titanium alloy design is to use cheap alloying elements to instead of expensive alloying elements without reducing the performance of the alloy. Iron has been considered for the development of few low-cost titanium alloys because of its stabilizing effect of the β-phase. Besides, it has a large solid solubility in β-Ti and owing to the atomic size difference with Ti can enable significant solution strengthening. But due to the high density of iron, high quantity of β-stabilizing elements and the formation of TiFe-based brittle intermetallic phases, welding joints of low-cost titanium alloys are prone to formation of cold cracks which is very important limiting factor for obtaining high quality welded joints with a strength of at least 90% compared to the strength of base material. Electron Beam Welding with its higher welding speed and intensity, can prevent formation of intermetallic and could help in obtaining welds with better mechanical properties, especially in combination with either pre-or post-welding heat treatment. The aim of this work is to study the effect of pre-heating and post-welding heat treatment on low-cost β-titanium alloy Ti-2.8Al-5.1Mo-4.9Fe welding joints by performing electron beam welding in combination with pre-and post-welding heat treatment. Specifically, this work will help to understand the influence of such techniques on the structure, phase composition and mechanical properties of low-cost β-titanium alloy welded joint.

Reducing Full-Field Residual Stress of Girth Weld With Thick Wall by Combining Local PWHT and Water Jet Peening

Abstract In this paper, a new controlling method combined local postweld heat treatment (PWHT) and water jet peening (WJP) was proposed to reduce full-field residual stress of girth weld with thick wall. The finite element analysis with sequential coupling method and experiment measurement were performed to study the residual stresses distribution before and after the new controlling method. The results show that the hoop and axial stresses through the thickness are all decreased greatly by using the new controlling method. As long as the new controlling method is used with appropriate parameters, the residual stresses on inner surface can be reduced from tensile stresses to compressive stresses, which greatly improve the resistance ability to stress corrosion of inner surface.

FEATURES OF MICROSTRUCTURE FORMATION IN THE WELDED PIPE JOINTS DURING HIGH-FREQUENCY WELDING AND SUBSEQUENT LOCAL HEAT TREATMENT

The transience of heating and cooling processes during high-frequency welding (HFW) of pipes leads to the formation in the heat-affected zone (HAZ) of a coarse-grained strained bainitic and/or martensitic structure with high hardness. Local or volumetric heat treatment is used to correct the microstructure of the HAZ. The paper presents the results of a study of the structure and properties of welded pipe joints produced at the Vyksa Steel Works. It has been established that the microstructure of the welded joint of pipes made of low-carbon steels (not more than 0.07% C) is mainly bainite of lath morphology, and for steel with a high content of carbon (~0.3%) and manganese ‒ martensite. To estimate the temperature field in terms of the angle and thickness of the pipe wall during local heat treatment a finite element model was created. The paper shows that the use of the model made it possible to optimize the heating parameters during the local heat treatment of pipes of various sizes. The experiments on local heat treatment of pipes with a diameter of 325 mm, made from rolled products 8 mm thick of steel 09Г2С, showed a significant refinement of the initial microstructure of the HAZ, an increase in uniformity and the disappearanc of structural heat-affected zones. In medium carbon steels (~0.3% C) with a high manganese content, the thermal cycle of HFC welding leads to formation of martensite. The local heat treatment in the form of normalization does not allow one to exclude the formation of martensite in the segregation zones due to the high cooling rate. The local heat treatment of welded joints in pipes made of steel 30Г (Russian Standard) in the high tempering mode (650–700 °C), with preliminary cooling of the welded joint to a temperature below the completion of the martensitic transformation (in segregation zones ~50 °C), makes it possible to release the segregation martensite and form the microstructure of sorbitol there.

Clinching of inductively heated aluminum die casting

The aim of the investigations described in this article is to improve the clinching of aluminum die casting. The focus is on clinching an aluminum die casting alloy by local heat treatment and hence to join them in a process-safe manner. For this purpose, a heating strategy is used to warm up the die casting alloys to reduce temporarily and reversibly the elongation and the yield strength in the material. In preliminary investigations, three different heating strategies (heating plate, resistance heating and inductive heating) have been investigated. Induction heating has been selected as the most suitable method due to the short heating time and the production of crack-free clinch points. In this paper, two clinching tool systems (one with a flexible die, one with a rigid die) were used. For these tools, two inductors with different diameter were manufactured. The effects of each inductor and clinching tool on an aluminum die casting alloy, such as heating time and crack behavior, were investigated. Surface images of the clinch points in regard to the heat treatment temperature were analyzed. Furthermore, the characteristic parameters of the joints such as interlock, bottom thickness and neck thickness were examined. In addition, the strength of the joined parts was investigated by head tension tests. The results of the developed method showed that it is possible to produce crack-free clinching joints below 6 s. Furthermore, the local heating led to an increasing interlock resulting in a 26% increase of the head tensile strength.

Local Heat Treatment of Goat Udders Influences Innate Immune Functions in Mammary Glands.

Heat stress and mastitis adversely affect milk production in dairy ruminants. Although the udder temperature is elevated in both conditions, the influence of this local temperature rise on milk production and immune function of ruminant mammary glands remains unclear. To address this question, we heated the mammary glands of goats by covering one half of the udder with a disposable heating pad for 24h, the other uncovered half served as a control. Sixteen Tokara goats (1-5 parity) and three Shiba goats (1-2 parity) at the mid-lactation stage were individually housed, fed 0.6kg of hay cubes and 0.2kg of barley per day, and had free access to water and trace-mineralized salt blocks. Milk samples were collected every 6h for 24h after covering (n = 16), and deep mammary gland tissue areas were collected after 24h (n = 5). The concentrations of antimicrobial components [lactoferrin, β-defensin-1, cathelicidin-2, cathelicidin-7, and immunoglobulin A (IgA)] in milk were measured by the enzyme-linked immunosorbent assay (ELISA). The localization of IgA was examined by immunohistochemistry. The mRNA expression and protein concentrations of C-C motif chemokine ligand-28 (CCL-28) and interleukin (IL)-8 in the mammary gland tissue were measured using quantitative polymerase chain reaction and ELISA, respectively. The somatic cell count in milk was significantly higher in the local heat-treatment group than in the control group after 12h of treatment. The treatment group had significantly higher concentrations of cathelicidin-2 and IgA than the control group after 24h of treatment. In addition, the number of IgA-positive cells in the mammary stromal region and the concentration of CCL-28 in the mammary glands were increased by local heat treatment. In conclusion, a local rise in udder temperature enhanced the innate immune function in mammary glands by increasing antimicrobial components.

Localized heat treatment to improve the formability of steel pipes for hydraulic applications: process design and mechanical characterization

In the present paper, authors have demonstrated how a localized induction heat treatment can be advantageously applied, controlled, and mechanically characterized on a specific part—i.e., on steel hose fittings for hydraulic applications. More specifically, the study shows how this specific type of heat treatment facilitates significant localization effects on mechanical properties, and how such a treatment could act as a powerful tool for material optimization in diverse applications. The instrumented micro-indentation test was adopted as the investigation method for mechanical characterization and, due to the reduced amount of material required for the test, has the double advantage of retrieving potential spatial gradients of the mechanical properties without causing permanent damage to the analyzed parts. A measurement of both Vickers hardness and plastic work are required in order to make the indentation necessary to quantify the strength and ductility capability of the parts’ materials. In addition, a customized tensile test, based on a strains measurement obtained through an optical full-field method—i.e., digital image correlation (DIC)—was developed with the aim of identifying and quantifying the correlation between the material properties attainable through a conventional tensile test and those measured by the instrumented micro-indentation test. Finally, it was demonstrated that the proposed customized tensile test, due to the localized heat treatment, is capable of retrieving potential spatial gradients of the material properties.

Influence of geometry on columnar to equiaxed transition during electron beam powder bed fusion of IN718

Correlation between spot-melt scan parameters (linear spot-density aka areal energy density), build geometry, and solidification microstructure evolution (columnar vs equiaxed) in a powder bed fusion technology is investigated. It is shown that to maintain the equiaxed solidification microstructure evolution in electron beam powder bed additive manufacturing (AM), the areal energy density per layer needs to be scaled with respect to the 2D cross-sectional area of the layer being melted. Samples with two different cross-sectional areas (40 × 40 mm and 20 × 20 mm) have been fabricated with varying areal energy densities. For a given square cross-section (20 × 20 mm), increasing the areal energy density (4.8 MJ/sq.m to 14.7 MJ/sq.m) transitioned the solidification microstructure from columnar to equiaxed. The observed microstructure data (Electron Back Scattered Diffraction - EBSD) is quantified by calculating the principal component (PC) score using a spatial statistics methodology. The sample with equiaxed grains is found to have a low PC score while the sample with columnar grain had a high PC score. A semi-analytical model is used to simulate the heat transfer and the local solidification conditions as a function of processing parameters (linear spot-density). The result from the heat transfer model is correlated with previously quantified microstructure data. Space-Time analysis of the melt pattern is done and correlated with the observed microstructure. In addition, from the findings, appropriate parameters have been used to additively manufacture a turbine blade with site-specific or hybrid solidification microstructure (traditional fabrication possible via a patented method of localized cold working and heat treatment).

Small Diameter Tube Post-Weld Heat Treatment Process with Brinell Hardness and Microstructure Inspection

The local post-weld heat treatment (PWHT) process test of 9Cr-3W-3Co small-diameter pipe welded joints was carried out using rope-type resistance heaters with different parameters, and the Brinell hardness test and microstructure observation were carried out on the welded joints after heat treatment. The results show that when the heating width was 200mm, the constant temperature was 790°C-800°C, and the constant temperature time was 2 hours, the Brinell hardness of the weld was in the range of 246HBW-265HBW, which had good performance. After tempering at 760°C-800°C, the welds all showed a clear tempered lath martensite.

Effects of High-Power Laser Heat Input on the Mechanical Properties of GPa-Grade Advanced High Strength TRIP Steel

Welding and local heat treatment with a high-power laser for GPa-grade transformation-induced plasticity (TRIP) steel were studied. When the focal length and scan speed were controlled under a fixed laser power, defect-free full penetration conditions were achieved at various heat inputs. The effects of laser heat input on the mechanical properties of the steel were evaluated. The results showed that a softened zone was lowered to 350 HV of hardness by tempered martensite under all laser conditions. As the heat input increased, the zone became wider. When an appropriate heat input of 20-60 mm/J was irradiated, the tensile strength and elongation were improved as compared with the base material. Under these conditions, the softened zone was significantly narrowed by the TRIP effect under tensile stress, and base metal fracture occurred. In addition, the laser increased the hardness in the weld metal and further activated the TRIP effect of the retained austenite. However, at a heat input of 90 J/mm, the TRIP effect was limited in the tensile test due to the wide softened zone and the increased hardness of sub-critical heat affected zone during the laser process. In this study, the effective heat input of the laser formed a full-penetration joint and locally enhanced strength and elongation simultaneously.

FEM Modelling of Tool Wear in Hard Turning Operations

Hard turning is a machining operation of finishing performed on material with a hardness higher than 45 HRC and it has been demonstrated to be a profitable alternative to grinding process allowing, respect to this latter, better surface quality, improved process control reliability, and faster production rates. The high pressure and sliding velocity at the tool-chip interface, in addition to the deformation energy generated, lead to the formation of high temperature zones localized in the cutting region. These thermal loads enhance harmful aspects on both cutting tool and machined material. On the tool, the abrasive-diffusive wear mechanism is promoted. On the workpiece, a local surface heat treatment of quenching is observed, upgrading the formation of a thin layer of over-quenched martensite, called white layer, due to its appearance under microscopical observation, that is undesirable due to its brittleness and related cracks generation. In addition to this, hard turning is usually performed in dry condition further augmenting machining temperature and tool wear rate. Because of the extremely high hardness of the machined materials, the employment of expensive ultra-high hardness cutting tools is mandatory. Thus, to make the process valuable, it is essential to optimize the tool usage by avoiding catastrophic failure and being able to forecast the tool wear evolution during cutting time as a function of the applied process parameters. One of the possible approaches for predicting the wear behaviour is finite element (FE) simulations of the turning process. In this work, the wear of polycrystalline cubic boron nitride (PCBN) tools when turning AISI 52100 hardened steel is investigated. An abrasive-diffusive wear model has been developed and implemented in a FE engine, by means of a dedicated subroutine able to update the geometry of the worn tool as a function of the cutting parameters, with the intent of simulating the tool wear behaviour, in terms of crater and flank wear extension. For the calibration of the model, the tool wear measurements achieved from an experimental campaign of orthogonal cutting tests have been used. The influence of process parameters on the wear rate has been examined, underlining that the most affecting parameter on tool wear is the cutting speed: the higher the cutting speed the higher the tool wear. Furthermore, it has been observed that the tool breakage was due to an excessive depth of the crater wear that modified the initial negative rake angle to a positive one. This modification changed the stress state of the tool from compressive to tensile, not well tolerated by PCBN tools, bringing to catastrophic failure. The tool wear simulation results are in good agreement with the experimental ones, validating the usability of the proposed computational methodology for crater and flank wear prediction. Therefore, the application of this technique allows the optimization of cutting parameters from a preventive FE simulation analysis avoiding the need of exploiting new costly and time-consuming experimental tests.

Effect of laser heat treatments on the hardness of tool steels

The application of laser heat treatments (LHT) has been growing attention in the last years, due to the effectiveness of localized hardening that can improve the tribological properties of steels. AISI P20 mod. steel is commonly used for plastic injection moulds applications and can be heat-treated to achieve high hardness values. This work presents an experimental investigation on the laser local heat treatments effect on the hardness of AISI P20 mod. steel parts, using a high-power diode laser. Different heat treatments at 1060 °C and 1100 °C using a feed rate of 10 mm·s-1 and 15 mm·s-1 were applied on the steel. The LHT were assessed through the hardness mapping trough depth and width. The results showed that the hardness of as-received P20 mod. tool steel is approximately 300 HV, and after LHT occurred an increment to around 625 HV with a fair hardness distribution. LHT had a minimum of 0.8mm and a maximum of 1.0mm depth.

An Economical and Mechanical Investigation on Local Post-Weld Heat Treatment for Stiffened Steel Plates in Bridge Structures

A heat treatment is effective for reducing the residual stress of the welded structures. A post-weld heat treatment (PWHT) requires a large heating apparatus (furnace). It requires a high energy, a long time, and a high cost. For examining the possibility of cost and energy saving in PWHT work, an economical and mechanical investigation of the local PWHT to stiffened plate members in steel bridges was conducted. The expense of apparatus for the furnace PWHT was 1.5 times higher than that of local PWHT by sheet-type ceramic heaters. When the number of heater units was reduced and were repeatedly used, the expense for the apparatus became lower. However, it took longer to complete the heat treatment than with the furnace PWHT or the local PWHT with full heater units. The thermal elastic-plastic finite element (FE) analysis examined the effect of local PWHT. The tendency of the stress distribution after the local PWHT differed from the welding residual stress or the stress after the furnace PWHT because of the temperature difference between the heated and the non-heated parts of the local PWHT. However, the effect of residual stress relief by the local PWHT could be almost the same as that of the furnace PWHT.

A Study of the Influence of Local Heat Treatment on the Structure of Welded Titanium Pipelines

The article analyzes the results of a study of the influence of zonal heat treatment on the structure of welded joints of pipeline elements made of titanium alloys Ti-3.5Al-1.5Mn. In the manufacture of such structures, the TIG welding method is used to join pipe elements, after which the heat treatment method can be used to relieve residual stresses. The experiments have confirmed the effectiveness of zonal heat treatment preceded by welding. It was revealed that for welded joints made of titanium alloys, heat treatment can stabilize the structure. In experiments conducted by the method of optical metallography, the structure of heat treated and untreated welded joints was investigated. The influence of heat treatment on the weld structure and heat-affected zone was identified.

A Near-Surface Layer Heat Treatment of Die Casting Dies by Means of Electron-Beam Technology

Increasing the service life of die casting dies is an important goal of the foundry industry. Approaches are either material- or process-related. Despite new material concepts, hot work steels such as H11 are still predominantly used in the uncoated condition for die casting dies. In order to withstand the stresses that occur, this steel is used exclusively in the quenched and tempered condition. Required properties such as high high-temperature strength and high hardness combined with high toughness are, in principle, contradictory and can only be adjusted consistently over the entire die by furnace-based heat treatment. However, the results of various investigations have shown that improvements in the thermal shock resistance and wear resistance of hot work tool steels can be achieved by thermally influencing the microstructure near the surface. Based on these studies and related findings, an approach to surface heat treatment using the electron beam was developed. Due to the particle character of the radiation and the associated possibility of high-frequency beam deflection, the electron beam offers significantly greater flexibility in energy input into the workpiece surface compared with lasers or induction. The overall technological concept envisages replacing furnace-based heat treatment in the production of casting dies by localized and demand-oriented boundary layer heat treatment with the electron beam. The experiments include, on the one hand, the experimental determination of a suitable temperature–time interval with a focus on short-term austenitization. On the other hand, a simulation-based approach of boundary layer heat treatment with validation of a suitable heat source is investigated. Regarding short-term austenitization, the corresponding temperature and time range could be narrowed down more precisely. Some of these parameter combinations seem to be very suitable for practical use. The test specimens show a hard surface layer with a depth of at least up to 6 mm and a very tough buffer layer. Numerical simulation is used to estimate the resulting metallurgical microstructure and the achievable hardness as a function of the temperature–time interval. In addition, the results provided show the possibility of determining and optimizing the material properties by means of a simulation-based approach within the framework of a purely digital process planning and subsequently transferring them into a process planning. In the technical implementation, a temperature control was first established by means of a two-color pyrometer. In the further course of research, the pyrometer will be supplemented by an internally installed infrared camera, which will allow the reproducible setting of specified temperature profiles even for complex, large-area contours in the future.

Numerical and experimental investigations on the temperature field in local post weld heat treatment of 9 % Cr heat resistant steel welded pipes

Local post weld heat treatment (PWHT) is usually employed in the field fabrication of large-sized 9% Cr heat resistant steel welded components, such as power plant boilers. Temperature field in local PWHT plays critical roles in both achieving PWHT purposes and avoiding detrimental effects of local heating. The objective of this research is to quantify the effects of local PWHT parameters and pipe dimensions on the temperature field in local PWHT of 9% Cr heat resistant steel pipes and finding the optimal process window to engineer desired weld properties. Finite element (FE) models were developed to simulate the temperature field of local PWHT and carefully verified by eight experiments using four 9% Cr heat resistant steel pipes with typical dimensions employed in ultra-supercritical (USC) boilers. The results show that the through-thickness temperature gradient is severely aggravated with the increase of pipe diameter and wall thickness, which will lead to inadequate tempering in the weld metal close to the inside surface of the pipe. To enlarge heated band (HB) width is an efficient way to mitigate the through-thickness temperature gradient, and the axial temperature gradient can be effectively relieved by augmenting gradient control band (GCB) width. The through-thickness temperature gradient is the major factor in implementing successful local PWHT for 9% Cr heat resistant steel pipes. A much smaller process window is found in 9% Cr heat resistant steel pipes due to their higher PWHT temperatures and narrower range of permissible PWHT temperatures.

A primary plus secondary local PWHT method for mitigating weld residual stresses in pressure vessels

Local post-weld heat treatment (PWHT) is often used for mitigating welding-induced residual stresses in pressure vessels and piping systems. As large and ultra-large pressure vessels are increasingly used in petrochemical and power generation industries, traditional local PWHT procedures stipulated in Codes and Standards become difficult to implement for some of the ultra-large vessels due to their very large diameter and overall length. In this paper, a new method referred to as primary-secondary heating based local PWHT technique (PS-PWHT) is proposed. Both finite element residual stress modeling and experimental residual stress measurements were performed for both validating the effectiveness of the proposed technique and elucidating the underling mechanisms. The results show that the PS-PWHT method can reduce welding-induced residual stresses in a significant manner, even leading to some level of compressive residual stresses at the vessel weld region.

Investigation of The Anisotropic Behaviour of Laser Heat Treated Aluminium Blanks

The continuous research for progressively lighter components moves the attention on the massive adoption of Al alloys. The achievement of such an ambitious goal passes through the definition of innovative manufacturing methodologies able to overcome some of the most hindering limitation of Al alloys, i.e. their poor formability at room temperature. A viable approach is based on the modification of the blank properties through a local heat treatment (to achieve an optimized spatial distribution of ductility/strength), so that the subsequent forming operation can be carried out at room temperature. The implementation of such approach relies on finite element simulations, where the use of a proper constitutive material model plays a fundamental role. In the present work an innovative methodology, already proposed by the authors in a previous research, is again adopted to enrich the characterization of a strain-hardenable Al alloy (AA5754), initially purchased in a pre-strained condition (H32), and locally annealed by means of a laser treatment: in particular, Thanks to the adoption of the DIC, the investigation of the anisotropy showed a strict correlation between the value of the Lankford parameter and the material condition reached at the end of the local treatment. The experimental data were fitted by a sigmoidal function and implemented in a modified Hill plasticity model for the simulation of the tensile test of a locally treated dogbone specimen, showing a good accordance with the experimental results.