Forming Limit Diagram Research Articles

Predicting the fracture forming limit of 5754-O aluminum alloy by finite element simulation

Abstract Aluminum alloy has the advantages of low specific gravity, easy processing and good welding performance, so it is widely used on automobile to achieve lightweighting. Forming limit diagram (FLD) is the most intuitive method for evaluating and analyzing the forming performance of aluminum alloys. Standard forming limit tests are complex and costly. To simplify test procedures of the formability of 5754-O aluminum alloys, three tests including uniaxial tensile, deep drawn cup and dome stretching tests are established through ABAQUS finite element software. The principal and secondary strain values at the time of fracture were extracted to construct the forming limit curve at fracture (FLCF). In order to verify the accuracy of the simulation results, corresponding experiments are conducted. The experimental results match the finite element simulation results, verifying the accuracy of the finite element simulation. The method presented in this paper can predict the formability of aluminum alloy quickly.

Numerical and experimental study of three-layered Al 1050/Mg AZ31B/ Al 1050 sheets formability considering strain and stress conditions through single point incremental forming

This article examines the formability of 3-layer Al 1050/Mg-AZ31B /Al 1050 sheets experimentally and numerically. Mg AZ31B, with its high strength-to-weight ratio, and Al 1050, with its formability and lightweight, are attractive industrial metals. In the experimental method, the forming limit diagram (FLD), the Forming limit angle (FLA), and the fracture depth were investigated for the 3-layer and base samples with two pyramid and cone geometries. The results showed that the ductility in the cone geometry is higher than that of the pyramid. Also, by comparing the FLD of the 3-layer sample to the base sample, the results showed that the formability of the 3-layer sample increased compared to the Mg-AZ31B base sample. In contrast, the formability decreased compared to the base sample of Al 1050. Numerical studies for predicting the FLD using the SPIF method were carried out using Abaqus software. The numerical techniques considered the second deviation minor strain (SDMIS), second deviation effect strain (SDEF), second deviation thickness (SDT), and second deviation major strain (SDMS). The results showed that the highest accuracy occurred for the SDT method compared to other numerical methods. To remove the effect of the strain path on the numerical analysis for predicting the FLD (from the stress analysis method), a second deviation of von Mises stress (SDVMS) was used. By examining the results, it was found that the results of numerical methods considering stress could be highly accurate.

Forming limit and failure behavior of fiber metal laminates under low-constraint conditions

Fiber Metal Laminates (FMLs), as high-performance composite materials, demonstrate exceptional potential in a wide range of applications, such as aeronautical and astronautical industries. However, the traditional cured FMLs possess complex interlayer stresses and low forming limits, restricting further promotion and application of FMLs. Low-constraint FMLs exhibit a lower forming resistance and better formability due to no curing during the forming process; however, the formation mechanism and response are not clear. This paper presents the Forming Limit Diagram (FLD) of low-constraint GLARE (glass fiber reinforced aluminum laminates) based on the forming limit test, and compares it with the conventionally cured laminates to evaluate the differences in the forming limit. In addition, combined with the analysis of failure mechanism and micro-deformation mechanism of specimens, the influence of different temperatures (20–80 °C) and forming states (width) on the deformation performance of laminates is further explored. The results reveal that the forming limit curve of low-constraint laminates shifts up with the increase of temperature, the forming limit initially increases with the increase of width, then followed by a gradual decrease, and the maximum principal strain of low-constraint laminates is increased by 29% at 80 °C compared to 20 °C. The cured laminate has a principal strain range of 0–0.02, while the low-constraint laminates have a principal strain range of 0.03–0.14. Compared with cured laminates, low-constraint laminates possess a higher forming limit due to the improvement in deformable degree between layers by resin flow and fiber slippage, which enhances their formability. This study is expected to serve as a reference for establishing forming limit criteria and optimizing forming schemes for low-constraint laminates.

Single-point incremental formability of Monel 400: Coupled grey relational and principal component analyses

This study reports the effects of single-point incremental forming (SPIF) process variables like vertical step down (0.2, 0.4, 0.6 mm), tool diameter (6, 8, 10 mm), feed rate (300, 600, 900 mm/min), spindle speed (300, 450, 600 rpm), lubricant (dry, oil, grease) and sheet thickness (0.6, 0.8, 1.0 mm) on the formability of Monel 400. Based on the varying wall angle tests conducted, it was found that the vertical step down was the parameter most influential in achieving maximum wall angle. The forming limit diagram constructed with the data obtained from straight groove tests revealed the parameter combination for low, moderate, and high formability while forming along different directions (0°, 45°, 90°). Also, it was observed that the formability has been positively influenced by increased tool diameter in the case of 0° orientation, spindle speed in the case of 45° orientation, and vertical step down in the case of 90° orientation. Based on the fractography study, it is concluded that more number of voids enhanced the forming limit. This may be due to the coalescence of voids and their slow aggregation. Based on the combined grey relational analysis and principal component analysis, it is obtained that the order of influencing parameters is vertical step down, tool diameter, sheet thickness, spindle speed, lubricant, and feed rate for obtaining the maximum sum of strains (0°, 45° 90°) and maximum wall angle.

Development of the forming limit diagram for fiber-reinforced thermoplastic composites and its temperature effect

The aim of this study is to investigate the formability properties of thermoplastic composite sheets and to develop a forming limit diagram (FLD) for them under ambient and elevated temperatures. Polypropylene thermoplastic composite sheets reinforced with unidirectional continuous glass fibers in a four-layer 0–90 layup were used in this research. Experimental findings demonstrate that the failure of samples at room temperature is more similar to brittle failure and occurs suddenly, whereas at elevated temperatures, the failure resembles ductile failure and occurs gradually. Employing the Nakajima method, a forming limit diagram for the composite material was successfully established at both ambient and elevated temperatures. The resultant forming limit diagrams illustrate an augmented strain tolerance of the material at elevated temperatures. Notably, despite the increased depth of stretch observed at elevated temperatures in comparison to ambient conditions, a concomitant reduction in the force requisite to induce deformation is evident.

Microstructure characterization and formability assessment of electron beam welded Nb-10Hf-1Ti (wt.%) refractory alloy sheets

Formability study on welded blanks of Nb-based refractory alloy C-103 (Nb-10Hf-1Ti (wt.%)) has tremendous potential for utilizing smaller sheets for realization of large-size divergent portions of upper-stage liquid engine nozzle of satellite launch vehicles and thrusters of attitude orbital control systems. In this work, vacuum-annealed monolithic C-103 sheets were electron beam welded successfully to obtain defect-free welds and detailed microstructural and mechanical characterizations were investigated. Columnar epitaxial grains were found in fusion zone (FZ) instead of equiaxed grains in base metal (BM). Detailed SEM and HRTEM analyses revealed spherical shape of nano-sized HfO2 precipitates with monoclinic crystal structure in the C-103 sheet. Further, microhardness across the weld cross-section indicated that the FZ had a uniform and maximum hardness of ∼195 HV0.5 due to formation of finer nano-sized HfO2 precipitates with higher number density, followed by a lowering of hardness in a narrow heat-affected zone. A marginal reduction in tensile strength of ∼6% with a considerable decrease in ductility of ∼29% was noticed for the welded sample. However, fracture occurred in the BM region, indicating good weld integrity. Furthermore, formability of the welded blanks was evaluated in terms of limiting dome height (LDH), forming limit diagram, and deep drawn cup depth. The effect of the presence of WZ on the formability of the C-103 sheet was estimated under uniaxial, plane strain, and biaxial tensile strain paths for the first time, and the results were compared with the monolithic sample. It was noted that the failure limit of the welded specimens decreased compared to that of the monolithic sample, resulting in a lower LDH of approximately 69% and 62% when deformed along plane strain and biaxial tensile strain paths, respectively. However, a marginal variation in LDH was observed for the uniaxial strain path. Also, the welded blank had more resistance to material flow into the die cavity due to the harder weld region, resulting in a reduction of deep drawn cup depth by 52% than that of the monolithic blank. The overall results concluded that the presence of the WZ significantly affected the formability of the C-103 sheet, especially in plane strain and biaxial strain paths. However, the fracture was never found to be propagating along the weld line, indicating the ability of the weld to sustain large plastic strains. This study provides insightful information on the formability of electron beam welded C-103 sheets for the successful fabrication of space components.

Assessment of aluminium alloys’ formability by elevated temperature testing

Abstract This work presents an investigation of the warm formability of AA7075-T6 aluminium alloy sheets using both experimental and numerical methods. Forming limit diagrams (FLDs) can be created by plotting the failure criteria on a graph with two axes representing major and minor strains. Sheets with a grid can be used to quantify both large and minor strains. General techniques available for the grid involve regular patterns of circles in this experiment. Experiments were conducted at various temperature levels, including room temperature, 100, 120, 140, 160, and 180 °C, as well as different strain rates. The investigation has revealed a significant impact of temperature on formability, while the effect of forming speed is quite insignificant across the whole range studied. At an ageing temperature of 140 °C, the distribution of precipitates is evenly balanced, resulting in improved mechanical strength. To offer accurate numerical models for warm-forming processes, a proposed constitutive model is introduced for aluminium alloy sheets. The present model incorporates plastic anisotropy and the effects of temperature and strain rate dependence. An investigation was conducted on the stress-strain behaviour of thin sheets composed of AA7075-T6 aluminium alloy under elevated temperatures and different strain rates. The objective was to ascertain the appropriate fitting parameters. It was associated with ABAQUS finite element modelling. The recommended material model was utilized to build finite element models, which were subsequently compared to the experimental data. The findings obtained from simulated isothermal uniaxial tensile tests were compared to the empirical measurements. The models used in the tensile test accurately predicted the material’s mechanical response. The predicted failure location, punch forces, and strain distributions for all three forming processes were found to be in close agreement with the experimental results. During deep draw operation, the warm forming limit curves were utilized to precisely predict both the pierce depth at which failure occurs and the precise location where the failure initiates.

Numerical Analysis and Application of Marciniak and Nakazima Experimental Model on the Formability of 304L Sheet

Abstract The comprehensive strength, ductility and high work hardening rate of 304L stainless steel contribute to its excellent mechanical and forming properties. This steel alloy is further distinguished by its notable corrosion resistance, high and low temperature capabilities, and excellent welding performance, making it a widely utilized material in industries such as petroleum, chemical, and nuclear power. In this study, we developed a simulation model based on the testing methods of Marciniak and Nakazima. By incorporating a constitutive model for ductile damage into our simulations, we made predictions regarding strain damage and failure under three different types of strain paths: uniaxial tension, biaxial tension, and plane strain. The results obtained from our finite element analysis were then utilized to generate the Forming Limit Diagram (FLD), which provided valuable insights into the material’s behavior under various forming conditions. Highlighting key differences in the simulation results between the Marciniak and Nakazima test methods. Additionally, the study included a comprehensive simulation verification in the context of bending forming analysis. Notably, the results of the bending analysis fell within the safe range, establishing a solid theoretical foundation for subsequent plate forming and risk assessment.

FABRICATION OF AA1100/Fl2O3 COMPOSITE STRIPS AND THE IMPROVEMENT OF THEIR ELECTROMAGNETIC, MECHANICAL AND FRACTURE PROPERTIES

In this study, forming limit diagrams (FLDs), fracture toughness (FT), mechanical, magnetic, and electro-physical properties of Al/Fe2O3 composites have been investigated experimentally. Accumulative-roll-bonding (ARB) process was used to manufacture composite samples. Then, Al/Fe2O3 composites have been produced at 300∘C up to eight ARB passes. Also, magnetic composites have been fabricated with 0, 5% and 10[Formula: see text]wt.% of particles. The interlayer bonding quality was improved at higher passes. By studying the SEM rapture morphology, it was shown that the rapture mode changed to shear ductile for samples with more passes. For composite samples fabricated at higher passes and in comparison with the annealed sample, elongated dimples were turned to shallow dimples. FLDs area as the main forming criterion dropped severely after pass one and then began to improve at higher passes. Fracture test results showed that after the 8th pass, the value of FT improved gradually to the maximum value of 34.3[Formula: see text]MPam[Formula: see text].

Delamination free forming of novel high interface strength metal-polymer laminates

A new class of metal-polymer-laminates, fabricated using wire mesh and “steel-chips” interlayer, is shown to have significantly high interface strength. A finite element model, calibrated using tensile, lap shear, and peel tests, is used to predict the deformation and failure of the laminates. Formability of the developed laminates is studied using the limiting-dome-height tests. The metal-polymer-laminates do not delaminate in any of the tests. A complete shift of forming-limit-curve towards biaxial-tension region is observed in strain-based forming limit diagram for the polymer side. Strain-path independent forming-limits are plotted in stress space, to negative the effect of non-proportional strain histories.

GTN poroplastic damage model construction and forming limit prediction of magnesium alloy based on BP-GA neural network

During plastic deformation processes, the ductile solids damage and fracture at the microscopic level originate from the evolution of micro -voids, including nucleation, growth and coalescence of voids. In this study, the fracture caused by damage of the AZ31 magnesium alloy sheet is analyzed using the Gurson-Tvergaard-Needleman (GTN) model. The damage parameters of the GTN model are determined by statistical void volume fractions (VVF) in three damage stages during uniaxial tensile experiments with scanning electron microscopy (SEM). The damage parameters are then optimized by the Back Propagation-Genetic Algorithms (BP-GA) neural network. According to the result, the main GTN damage parameters: the initial void volume, the critical volume fraction, the void volume fraction of the nucleation part, and the void volume fraction when the material finally fails are obtained, respectively. Comparing the simulation with the test, the results of the optimized parameters fit better. The void growth reflects the damage during the deformation process, and the GTN model can accurately predict the ductile damage. Furthermore, the experimental forming limit diagrams (FLDs) of the AZ31 sheet at 200℃ are accurately predicted using the parameters obtained by the GTN model. Good agreement has been observed between the experimental and predicted FLDs.

Multipoint forming process of aluminum sheet considering its forming limit diagram: Experimental and numerical investigations

Multipoint forming process of aluminum sheet considering its forming limit diagram: Experimental and numerical investigations

Effect of strain state on the surface roughening for hydroforming of aluminum alloy tube based on cross-scale numerical modeling

The complex deformation behavior would result in surface roughening such as orange peel defect during the hydroforming process of aluminum alloy tubular parts. In order to control the surface quality of hydroformed tubular parts, the effect of strain state on the surface roughening for 2219 aluminum alloy tube was analyzed based on a cross-scale model. The model combined the crystal plasticity model and macroscopic finite element model. During the uniaxial tension, the surface morphology reveals an equiaxed pattern characteristic of orange peel due to the strain incompatibilities between grains, and the peak and valley are stretched along the tensile direction. The surface roughness under tension-compression plane strain state is the lowest due to the low through-thickness strain. In the biaxial tension region, the change rate of surface roughness gradually increases with the decrease of the second principal strain especially in the late deformation stage, and the surface features evolve from an orange peel pattern to a ridging pattern. The forming limit diagram under different strain states based on surface roughness was established to guide the optimization of hydroforming process. Compared with the one-step hydroforming, the surface roughness of the bulging peak of 2219 aluminum alloy tube using multi-step hydroforming with the axial self-feeding decreases obviously from 16.3 to 10.8 μm due to the significant reduction of the equivalent strain.

Development of forming limit diagrams for motorcycle fuel tank made from AA5754-O under deep drawing

The research studied forming limit curves (FLC) for aluminum alloy 5754-O (AA5754-O) and modified them using two methods. These methods aimed to create FLCs for application in describing the forming behavior of sheet metal material through a deep drawing process simulation in the PAM-STAMP program. The methods are as follows: The Nakajima test combined with a new method, a novel process for grid creation on the specimen: laser marking combined with elastic paints. A mathematical material model using the fracture model along with the yield criteria: YLD2000-2D and hardening law: Swift-Voce. The Keeler-Brazier modified equation was chosen as the fracture model for this research because it is an effective equation for creating FLCs for steel materials and has not yet been applied to aluminum materials. Furthermore, no one has previously used the Keeler-Brazier modified equation in conjunction with YLD2000-2D and the yield criterion Swift-Voce hardening law. In summary, the FLC generated from YLD2000-2D, Swift-Voce hardening law, and Keeler-Brazier modified equations can predict the location of damage occurrence on the motorcycle fuel tank, which occurs due to the deep drawing process, using finite element simulation accurately. This closely resembles the actual forming process in the industry.

Effect of ARB process on the plane stress fracture toughness, creep properties and forming limit diagram of Aluminum/BN/Copper composite strips

Abstract In the present study, Al/BN/Cu bimetal composite strips were fabricated via the accumulative roll bonding (ARB) process. Then, fracture toughness, mechanical properties, bonding strength, forming limit diagram (FLD), and creep properties have been studied via experimental techniques. The study of creep behavior and mechanical properties showed a formation of a 17 μm atomic diffusion layer at the interface during ARB under three creep loading conditions namely 35 MPa at 225 °C, 35 MPa at 275 °C, and 30 MPa at 225 °C. The tensile strength of samples improved to 144 MPa which was about 234% in comparison with the primary Al monolithic sample. It was observed by the SEM that the fracture types changed to shear kind after higher passes including prominent effects on the fracture morphology. FLD curve dropped severely after the first ARB pass and then began to enhance at higher passes. The fracture toughness value of 30 MPa m1/2 was achieved after ten ARB passes. An intermetallic composition was created near Al. The creep failure time did decline by 44% and the stress level decreased by 13% at a constant temperature. It can be concluded that applied temperature and stress effect on creep properties especially leads to increasing the slope of creep curves with higher stresses. This trend was opposite for the creep temperature at higher temperature levels. Moreover, dynamic recrystallization was observed through the crystalline structure of samples.

Forming limit diagram of annealed copper OFE thick sheets for optimized hydroforming of superconducting RF cavities

Coated superconducting radio-frequency (SRF) cavities are planned to be implemented in the Future Circular Collider (FCC) at the European Organization for Nuclear Research (CERN). The interest in industrialized and high-performance processes for fabrication of the corresponding copper substrates has thus risen. Tubular hydroforming is a well-known industrial process, but has not been thoroughly applied for ultra-pure oxygen-free electronic copper (Cu-OFE) thick products. To provide a feasibility analysis for the optimized fabrication process of copper substrate seamless cavities, a Forming Limit Diagram (FLD) of the material of interest was studied. In this paper, the methodology, test results and initial benchmark of the material model is presented, for 4 mm and 2 mm thick sheets.

A strain components-based Mohr–Coulomb fracture criterion for proportional loading

Ductile fracture criteria are crucial in the application of elastoplastic materials like advanced high-strength steels, particularly due to their tendency to fail without significant localized necking. It is aimed to figure out the unified mechanism for ductile fracture and accurately describe it with phenomenological criteria. In this study, the effect of the stress triaxiality and the Lode parameter is analyzed mathematically. The maximum shear strain and the normal strain to fracture are emphasized in the proposed strain components-based Mohr–Coulomb fracture criterion particularly designed for plane stress states, and it is assumed that fracture occurs when the combination of the maximum shear strain and the normal strain reaches the critical value. It is then extended to describe fracture with the equivalent plastic strain and the normal strain to fracture. The experimental fracture data of AA 2024-T351 and the additively manufactured Ti-6Al-4V titanium alloy are used to verify the proposed models. A fracture forming limit diagram comprising forming limit curves calibrated from stress states under different stress triaxialities is proposed based on the proposed fracture criteria for plane stress states. This study shows that a strong correlation between the maximum shear strain and the normal strain to fracture has been observed, and it can be described piecewise-linearly. Besides, the orientation of the fracture surface under both tension (including plane strain tension) and compression (including plane strain compression) can be qualitatively explained by the Mohr’s strain circles. The results provide a new insight into the intrinsic deformation and fracture mechanism of materials that fail without severe localized necking.

Investigation and optimization on the formability of aluminum 1050/stainless steel 304L bilayer sheets fabricated by cold roll bonding considering the Box-Behnken method

Composite metal sheets have found extensive applications thanks to their high corrosion and wear resistance, as well as greater strength, stiffness, and formability relative to the base sheets. Stainless steel composite sheets account for over 80% of the metallic composite sheets. Their higher performance and lower costs have increased their applications in the food and automotive industries. This study experimentally addressed the formability of the Al 1050/Stainless Steel 304 L bilayer sheets prepared through the cold rolling process. After designing the experiment using the response surface method, considering the layer thickness and reduction ratio of the rolling process, the bilayer sheets were prepared using the cold roll bonding process. Formability included the forming limit diagram, the magnitude of FLD0, and elongation, which were derived by Nakazima and tensile tests. Then, the formability was optimized as a function of input parameters considering the Box-Behnken method. To this end, a new criterion was presented to compare the formability of the sheets. This criterion can be used to assess the formability of a sheet considering various loading modes. Microstructural observations justified the variations in the formability of the bilayer sheets against the input parameters, i.e., thickness ratio and reduction ratio. The results indicated that the formability of the Al 1050/Stainless Steel 304 L bilayer sheet (i.e., safe forming region) reached its maximum value at tAl=4mm;tSS=0.8mm;andr=45%.

AI-assisted prediction of St14 steel sheets formability: Neural-fuzzy systems and crystal plasticity assessments

We've introduced a new technique leveraging artificial intelligence to determine in-plane forming limit strains in St14 sheet metals. A neural-fuzzy AI system was devised to predict safe points on forming limit diagrams, considering aspects like crystal texture, metal sheet thickness, and spherical punch diameter. Neural-fuzzy systems could be utilized in prediction of forming limit curves using linguistic data description. To obtain the data required for training the AI network, in-depth tests, including XRD, metallography, tensile testing, and Nakazima's hemisphere evaluations, were carried out to detail the metallurgical and mechanical properties of St14 sheet metal. Data on texture, the tensile curves, and grain morphology were then incorporated in crystal plasticity models to find hardening constants for St14's single crystals. Using these determined values, Nakazima's tests were replicated through multi-crystal aggregate configurations. We then undertook a comprehensive parameter investigation via 324 crystal plasticity simulations to shed light on the effects of texture, sheet depth, and punch dimensions on St14's formability. This rich dataset paved the way for training an adaptive neural fuzzy inference system (ANFIS), leading to substantial reductions in time and computational needs. The results validate that the ANFIS model offers accurate and reliable predictions, highlighting its viability for wider use in determining forming limit diagrams.

Investigation of the influence of plane strain constrained anisotropic plastic flow on the localized necking prediction

PurposeThe purpose of this manuscript is to investigate the influence of the satisfying of plane strain conditions on the prediction of the localized necking and to evaluate this effect by the different hardening models.Design/methodology/approachHigh-order anisotropic Drucker yield function, two types of hardening models, namely Hollomon power and Voce saturated, and the modified maximum force criterion (MMFC) are employed to predict the forming limit strains of AA3104-H19 alloy. Two identification methods, namely conventional and plane strain constrained, are applied and forming limit diagrams of the material are predicted by the incorporation of the anisotropic Drucker criterion and the hardening models into the MMFC for both calibration methods.FindingsThe enhancement in the prediction accuracy of the forming limits provided by the implementation of the plane strain constrained method is strongly dependent upon the selected hardening model type in the MMFC. About 18% improvement in the prediction of the biaxial limit strains is provided via Hollomon power law hardening, whereas the opposite result is occurred in case that the Voce saturated hardening law is used, and the predictions match with the experimental data only in the plane strain point and its surroundings.Originality/valueThe plane strain constrained identification method precisely predicts the location of the plane strain point on the yield locus and also any yield stress or anisotropy coefficient in the plane strain state is not required during the calibration, therefore the method can reduce the number of the required experiments for the constitutive characterization, and it will be attractive for both academy and industry. Additionally, the improvement in the prediction of the biaxial forming limits can be provided by applying of this method along with the appropriate hardening law.