On the backward design—an advanced concept for the design of welded structures for demanding applications

Conventionally, the design of welded structures is based on the properties of semi-finished products, such as rolled plates and strips. The effects of manufacturing processes on the material properties, such as cold forming and welding, are neglected or they are controlled by the limitations on manufacturing parameters. However, such conventional approaches do not obtain desired solutions for the end users in terms of performance of the end product. This is the case, particularly when using high-strength steels, in which the manufacturing processes can remarkably change the properties of semi-finished products, and the production quality must fulfill higher criteria compared to the structures made of low-strength or mild steels. Consequently, a new approach called backward design (BD) is established to obtain better properties for end-products and to develop more purposeful steels, improve quality in design and manufacturing, and minimize the lead time in the whole production chain. The BD concept is based on the needs of end-users and exploits simulations and digital twins, considering the whole production. However, the optimization of production, including all its adjacent phases, is a comprehensive multi-parametric task, and, thus, it will be always a compromised solution. Nevertheless, the BD concept provides a new way of thinking about the whole production, not only material but also the geometry of the construction and its fabrication phases. The issue is currently relevant because the steel industry will transform toward “green” steels (hydrogen-based reduction) and thus enable the creation of new tailored steels for end-products. In this paper, a general overview of this concept is presented.


Introduction
BD is a widely known concept in education [1]. Theoretically, the idea of BD can be applied in the production of new constructions and devices and, particularly, new construction materials for them. However, this idea can be realized now also in practice based on the simulation of production and digital twins [2]. One important application field is the design of welded structures for demanding applications, i.e., structures with high requirements in terms of structural performance.
Conventionally, the structures are first designed, then analyzed, and finally modified to fulfill the assumed loads by service. Using this approach, the strength of welded structures is based on the properties of semi-finished products, such as rolled plates, strips, tubes, and profiles. The semifinished products are modified into structural components and finally end-products through the workshop processes, such as blasting, cutting, cold forming, welding, and various finishing processes, as illustrated in Fig. 1. The most important material properties, such as yield and ultimate tensile strength (UTS) and elongation, are also standardized and fulfilled by the semi-products. In this approach, the effects of manufacturing processes on the material properties, however, are ignored, or manufacturing parameters are controlled by given some limitations such as the degree of cold forming in bending, or cooling rate in welding. The cold forming is controlled by a minimum allowable radius/ thickness ratio, usually given by steel manufacturers, and the critical cooling time (t 8/5 ) range is controlled by the welding heat input related to joint geometry [3,4].
Nevertheless, this approach does not obtain desired solutions for the end-users in terms of the performance of end products. This is the case, particularly, when using highstrength or ultra-high-strength steels (HSSs or UHSSs), for which the manufacturing processes can remarkably alter (i.e., weaken) the properties of semi-products. In addition, the requirements for the quality in design and fabrication with HSSs and UHSSs are at a higher level compared to structures made of low-strength or mild steel. Consequently, a new approach based on the BD is established for steel structures. In the BD concept, the needs of end-users give guidance for the whole production from steelworks to service and recycling. The applications of the BD concept provide a digitized model of production since the simulation of consecutive process phases must be carried out in a reversed order. The optimization of the production, including all its phases, is a comprehensive multi-parametric task, and thus, it always results in a compromised but potentially optimized solution. Nevertheless, the BD concept provides a new way of thinking about the whole production, not only material but also the geometry of the construction and fabrication phases.
In the conventional workshop processes, the material performance characterized by "Property X" (Fig. 2) is affected by the manufacturing processes. In this context, this property can refer to many technical requirements required from the end product, such as tensile strength, ductility, fatigue capacity, buckling strength, or stiffness. In some of these requirements, the workshop processes do not necessarily highly affect these properties, e.g., stiffness and buckling strength, since they are affected by the geometry of the component. Nevertheless, in some other characteristics, such as fatigue and ductility, the properties might be highly influenced and governed by local properties in weldments. From the product design, analysis, and design of fabrication viewpoint, the initial property condition in the intermediate plate, bar, or tube is the design parameter. To have sufficient properties in an end product, the fabrication phases are ruled by various limitations and requirements given in manuals, material specifications, or user experience. In the field of welding, this applies, e.g., applicable welding processes, consumables, parameters and subsequent cooling rate, and/or time (such as cooling time from 800 to 500 °C, t 8/5 ) and preheat temperature T 0 . In other manufacturing steps, the cutting processes, speed (v cut ) and applied gas, or forming limitations (the inner radius to the plate thickness ratio, r i /t) are given. The basic concept is that by following these requirements, sufficient properties in the end product can be obtained.
In the BD concept, the starting point for the design is the requirements for the end product. Usually, there is a certain accepted range for the property, between the minimum value and over quality (Fig. 2). Subsequently, the manufacturing steps are modeled and simulated, and thus the property range can be reversely obtained. In addition, similar properties in the end product can be acquired using different steel grades, as shown by alternative routes in the workshop processes. When the effect of workshop processes on the material properties is understood, the purposeful steel can be chosen. For simplicity, Fig. 2 only exemplifies the property ranges covering only an individual property. In most cases, multiple criteria must be fulfilled, and thus the material selection requires a consideration of various properties. Nevertheless, the BD concept can be used for this optimization since the influence and interaction of workshop processes are known. Furthermore, the quality and its variation in end products can be enhanced, and potentially the lead time in the whole production can be diminished as the manufacturing parameters can be optimized. The aim of the current work is to conceptualize different steps in the whole BD system and provide actions for further studies that are taken in an ongoing research project at LUT University named Fossil-Free Steel Applications (FOSSA).

General description
The BD concept is initiated from the needs of end-users to create an optimal solution for service. The approach provides  Fig. 1 Typical production chain of a welded steel structure simulation tools and simultaneously, a digital twin of the production is available. The description of the highly varying needs and properties of an end product is a key issue for the process, and it concerns the requirements for the geometry, material properties, and manufacturing parameters, as illustrated in Fig. 3. It means that the procedure is partly dependent on the available workshop capabilities, resources, and applied manufacturing processes and, consequently, cannot be a fully generic approach. The simulation of workshop processes is mainly based on numerical methods, i.e., nonlinear finite element analysis (FEA), but statistical approaches are also applied, particularly when the steel mill processes are defined. The material simulation can be based on the multiscale material modeling by FEA, or the results can be collected from an artificial neural network (ANN) approach. However, when applying virtual approaches and simulations, experimental tests are always needed to verify and validate the simulation models.
The requirement matrices for BD design consist of the loading and material properties considering also the environmental conditions, e.g., working at low or elevated ambient temperatures.

Structural analysis
The BD concept is based on the analysis of service (needs). Unfortunately, the service period, with its high varieties, has been and will be the most challenging phase to predict in the lifecycle of a product due to the case-specific features of each product. From the conventional viewpoints, this has been considered by the different safety factors, consequences of failures, and survival probabilities. The loading history of an end-product during the service should be identified in terms of the maximum and minimum load values, fatigue equivalent, and required fatigue life (cycles). In addition, the type of loading in terms of stress/strain ratio

Rolling Mill
Rolling parameters is an important design parameter. The design loads can be defined based on the experiments, using recorded load histories for similar constructions in the same working environment, or numerical simulations. In fact, the simulation of loads can be conducted using a rather simple mechanism model, and subsequently, the stresses can be defined after creating the purposeful local geometry for the construction using the sub-modeling techniques. In Fig. 4, a typical part of the load history defined by simulation and characteristic values from it is presented.

Structural design
The BD concept can be used to fix the minimum yield strength for an optimal steel grade by setting the capacity requirements from the static load conditions equal to the ones from fluctuating load conditions, Eq. (1). For simplicity, the case is presented for a bending-loaded structure shown with section moduli, but could also for other load components and corresponding cross-sectional dimensions, too.
where W static is the section modulus (requirement) for the static loads, γ L is the partial safety factor for static loads (1.5), γ M0 is the partial safety resistance of cross-sects. (1.0 or 1.1), f y is the yield strength of the material, W fatigue is the section modulus (requirement) for the fatigue loading, ΔM eq is the equivalent moment range, and Δσ is the (allowable) stress range that can be written as where FAT red is the reduced fatigue strength (considering, e.g., thickness correction factors, elevated temperatures, or enhancements by different residual stress states and postweld treatments [6,7]). γ Mf is the partial safety factor for fatigue strength (usually from 1.0 to 1.4 depending on the 3 BD concept can be applied to create more purposeful steels, constructions and workshop processes, and parameters for them. ε DOCF is the degree of cold forming (strain), f y,HAZ is the yield strength at the heat-affected zone (HAZ), A g,HAZ is the uniform elongation at the HAZ, K Ic is the impact toughness at the temperature T and strain rate ̇ , Δσ R is the fatigue resistance (strength) at the applied stress ratio of R, I is the second moment of inertia, W is the section modulus, and FAT red is the reduced fatigue strength Fig. 4 Part of the loading history of a boom mechanism produced by simulation or by measuring the existing structure design strategy and consequences of failure [6,8]). Combining Eqs. (1) and (2), the yield strength requirement can be written as where ΔM th is the minimum (threshold) value for the effective moment range in fatigue loading, ΔM max is the maximum moment range of loading, ΔM i is the individual moment range (see also Fig. 4), n i is the number of cycles at the ΔM i moment ranges, and N ref is the number of cycles (or other units) at the reference period. The M max and ΔM eq values in Eq. (1) can be defined by simulation, as illustrated in Fig. 4.
If lighter structures can be utilized in terms of improved energy efficiency or reduction of emission, much higher steel grade than defined by Eq. (3) can be chosen. In order to get more benefit from the usage of HSSs and UHSSs, the quality of critical details must be at a high level, as the fatigue strength does not improve along with the increased material strength. The improved quality can be realized by a proper structural design together with using optimized welding parameters or post-weld treatments (PWTs), and the quality is considered in the calculation of the FAT red value. After determining the steel grade, an optimal crosssection based on service loading can be defined. In some simple cross-section cases, such as in the bending loading, the optimization can be carried out through a closed-form solution but in the general case, a numerical analysis is required. If a steel grade with a higher yield strength is chosen, a more complicated cross-section is needed compared to normal-strength steels in order to avoid the local buckling of the cross-section and to keep the stiffness of the cross-section as required. The multi-corner cross sections with thin wall thickness can obtain good strength, stiffness, and stability properties as a beam, but e.g., distortions of the cross-section can be then the weakest link of strength and should not be ignored. Secondary stresses due to buckling should be avoided in structures subjected to fluctuating load and cross-section class 3 [9] should be thus preferred. First, the purposeful cross-section shape must be created, and then the dimensions should be fixed so that the stiffness and section modulus W fulfill the requirements with a minimum cross-section area A. An example regarding the cross-section dimensioning is illustrated in Fig. 5. Thus, the BD concept is applied to convert the needs from the end-use to purposeful steel grade and dimensions of the designed structure.
Furthermore, a structure can be designed asymmetrically, e.g., in such approach that the side of beam, where geometrical discontinuities do not exist, is subjected to cyclic higher stress than the opposite side of the beam. This can be formulated as follows: In Eq. (4), Δσ det A and Δσ det B represent the critical stress ranges in locations of details A and B, and FAT det A and FAT det B are the fatigue performances at the same locations, respectively. The stresses and FAT classes can represent any local or global stress values. This example represents BD application for both design and manufacturing purposes (see Sect. 2.5).

Material design
After obtaining steel grade based on the service load, the other material properties needed by end-users can be defined. Steel industry is going toward fossil-free (FF) produced steels by using hydrogen in reduction process [10]. Since this new technology increases production cost compared to conventional coal-based steel production, use of FF steels will push industry toward minimizing the use of steel by means of providing HSS and UHSS options. These new innovations for renewing steel making process also obtain promising options for creating new tailored steels. This is an ideal case for applying the BD concept to set purposeful properties for tailored, FF-produced UHSSs (FFUHSSs). The semi-finished products can be seldom utilized directly in end products as they are first treated by many workshop processes. Consequently, the requirements for the tailored steels should be set from the service. Typically, there is a set of requirements, and consequently, it is a compromised combination of corresponding material properties, such as good cold forming and weldability, high yield strength, adequate uniform elongation, good impact toughness also at low ambient temperatures, suitability for hot-dip galvanizing.
In the BD concept, the chemical composition of steel and the rolling parameters in thermo-mechanical (TM) rolling including reduction rate and cooling, should be determined in a such way that the semi-finished product, after all the necessary workshop processes, fulfills the set of requirements. There are some numerical tools available for designing good semi-finished products by controlling the parameters in steel making, but this concept should be expanded to cover the workshop processes too, and most essential, it should be guided by requirements defined by end-users. This is the most challenging part of the BD concept because it covers all production phases. However, this is a novel idea to produce more purposeful steels to obtain the best properties for end-products in the service.

Manufacturing and workshop processes
The BD concept can be exploited also to guide and control the workshop processes. The quality of end products can be improved by using optimal parameters for cutting, cold forming, welding, and surface finishing, purposefully. The optimal parameters result in a required performance in the end product but also reduce the lead times during workshop processes, e.g., through the minimized need for repair and post-processing work. Another topic that can have an effect on the quality of end products is the sequence of processes, such as blasting-welding and cutting-forming. In welding, the sequence of welding passes is an essential aspect in terms of welding distortions and residual stresses. Eventually, the end-use will define which ones are more important quality parameters among others in the application and which quantitative effects they have, e.g., on the fatigue strength of the end product. The 4R method obtains a tool to estimate the residual stresses and effects due to misalignments and distortions on the fatigue performance of welded structures [11][12][13]. The anticipation and prevention of distortions is one application of the BD concept, and it can be applied to tack welding, as illustrated in Fig. 6, or to actual welding. The control of distortions due to tack welding in robotic welding is important because distortions define the root geometry for adjacent joint members, and thus, the anticipation enables high welding quality. FEA is widely used as a numerical tool for simulating residual stresses and distortions due to the welding [14][15][16][17] and post-weld treatments in association with the mechanical loads [18,19]. The results of those analyses can be used for establishing a digital twin for the workshop processes, which is one application of the BD concept. In addition, Eq. (4) is also valid for manufacturing purposes. For example, a lower stress range level can be designed for that side of the structure, where high-quality manufacturing is a challenging task to reach, or the welding sequences can be defined so that the residual  [16] stresses or distortions due to welding will be lesser at that side of the structure. One important application of the BD concept is the welding of HSSs and UHSSs. Cooling time from 800 to 500 °C, i.e., t 8/5 , defines the microstructure of HAZ according to the continuous cooling transformation (CCT) diagram of steel as illustrated in Fig. 7a. The cooling rate is controlled by the heat input Q, preheat/working temperature T p , and joint geometry. On the other hand, in single-pass welding, the heat input depends on the welding parameters and, thus, on the melted cross-section area of weld A w (see Fig. 7b). Throat thickness a is evaluated from strength calculations but it also controls directly the heat input in single pass welding and thus, strength properties at the HAZ. The throat thickness can be evaluated as follows [3,4,20,21]: where ß w is the correlation factor, t is the plate thickness, γ M2 is the partial safety factor for resistance of cross sections in tension to fracture (1.25), fu is the ultimate strength of material, σ x and τ xy are the normal membrane stress and shear stress components in the plate adjacent to the weld, respectively, α is the bevel groove angle (see also Fig. 7b), η is the thermal efficiency of welding process, U is the welding voltage, I is the welding current, v is the welding speed, and k is the material energy coefficient. For single-pass welding, k = 0.022 ± 0.005 kJ/mm 3 has been suggested based on the macroscopical evaluations [22]. As a result, the welding heat input can be written as For the 3D and 2D heat transfers, the cooling times can be evaluated by Eqs. (6) and (7), respectively. Consequently, the cooling rate can be evaluated based on throat thickness in single-pass welding [4]: and where F3 and F2 are the joint shape factors for the 3D and 2D cases.
The same cooling rate can cause distinguishing properties in nominally same steel grades depending on the manufacturing route of UHSS steels, namely direct-quenched (DQ) and quenched and tempered (QT) steels, as illustrated in Fig. 8 [23] due to the differences in the chemical compositions. These differences can have a great impact on the mechanical properties of welded components [25]. Consequently, such behavior must be included in the BD concept in terms of optimal cooling rate (via heat input) in order to receive optimal strength properties for end products. In the case of DQ steels, it means the optimum is a high cooling rate, but on the other hand, rather opposite goal for QT HSS is needed. In general, multi pass welding instead of larger single pass can obtain a method to control this effect.

Backward design and digital production
The BD concept requires experimentally validated simulation models of the products available, as illustrated in Fig. 9. Numerical models enable to make backward steps, which are needed when the requirements from end-use are focused on properties of semi-fished products as an initial step and subsequently considered optimal parameters in the steel making. In addition, the effects due to workshop processes must be considered. Each workshop uses its own processes or utilizes the potentiality of subcontractors, and those manufacturing boundary conditions must be considered in the BD concept. For example, novel FFUHSSs can be created to be ideal for laser welding, but they can be difficult to weld using gas metal arc welding (GMAW) processes. In order to avoid such obstacles, the limitations of workshop capabilities should be included in the analyses. The whole production chain and the effects of different processes can be demonstrated by stress-strain history. However, it makes sense to start the development with the most essential processes, e.g., by creating a simulation model from welding, and after that, by adding the other parts of the chain, step by step. In practice, the BD concept provides the digital manufacturing system to be available. Digital fabrication enables the production of high-quality steel structures and shortened lead times. The history of the production and its phases are controlled, for instance, by QR codes, in which the values of realized fabrication and working parameters are recorded and which are compared to values from digitized design. The implementation of a digital twin covering all production phases can be conducted by FEA simulations. Other Stress-strain history of the material in service Fig. 9 BD concept in association with the material modeling in different essential phases of the production options are statistical approaches and ANN applications. Furthermore, the statistical and ANN approaches can be combined with the numerical methods; for instance, the data can be produced by the numerical methods that are subsequently statistically analyzed or applied to build an ANN model for this step. The multiscale modeling of material obtains the most powerful tool for creating the simulation model for adjacent production phases and collecting their cumulative effects, which can then be utilized in the BD concept. However, material behavior in workshop processes and service is an extremely complicated and multilevel phenomenon that always requires experimental validation and verification.

Discussion and conclusions
The current work introduced the initial steps to establish the BD concept for welded structures. The main concept with the most important considerations was outlined, and further actions should be implemented to build a BD concept for real welded applications. Although the current work only exemplified the actions that should be taken, such BD applications are essentially needed in the future as they provide many advantages compared to the conventional approaches. Currently, the design and fabrication of welded structures have been based on the properties of semi-finished products, and sufficient strength and ductility for the end product have been met by introducing various limitations for fabrication parameters. In the field of the welding process, this covers, e.g., welding heat input, preheat, and inter-pass temperatures. Via the BD concept, new tailor-made and purposeful steels can be produced, and weldability can be considered in a detailed manner. For instance, a semi-finished product can have even lower properties in the semi-finished product if it results in higher, optimized, and purposeful properties in a welded end product. The aim of the BD concept is to provide the purposeful and required properties for the end product, not necessarily for semi-finished products. In a larger scope, the BD concept can also include the optimization of workshop processes and parameters in terms of welding quality [26], lead time, and productivity [27], as well as production cost [28] when the whole production is simulated. From the end-product viewpoint, the BD concept provides great opportunities to obtain the best solution with multiple criteria: energy efficiency, emissions, and structural performance. Figure 10a illustrates a welded bracket in a boom construction made of DQ UHSS. Based on multibody simulations of the end-use of the boom construction, the load history and direction of the bracket force F can be defined so that it will assess the required throat thickness for the fillet weld. It is noticeable that the load case with the maximum force F max is not necessarily the most critical for weld sizing, but the acting force direction must be considered too. In the exemplified case, the required fillet weld size is 8 mm. The perimeter of the bracket weld, i.e., the total weld length, is s, and the welding process is robotized GMAW, and the welding will be conducted in the flat-horizontal (PB) position, Fig. 10b. However, the throat thickness of 8 mm requires three welding passes, which increases the lead time of the manufacturing process. By reshaping the bracket, the weld perimeter length can be increased in this case by 25%, which obtains the required throat thickness of 6 mm. Such throat thickness could be prepared with robotized welding using a single pass in the PB position. The use of single-pass welding obtains the optimal productivity (increase of roughly 140%) for this production state. However, this means relatively high heat input in welding (more than Q > 1 kJ/mm), which results in a low cooling rate with the existing joint geometry and thus causes softening in the a8 HAZ in the vicinity of the weld. Since designers are responsible for welding sizing and usually not for the number of welding passes, a welding expert, in a collaboration with the design engineer, changes the detail to be conducted by two welding runs. The parameters for the first pass are fixed to ensure sufficient weld penetration, and the parameters for the second pass are defined to create a smooth transition at the weld toe. This procedure provides a high cooling rate and thus avoids the softening in HAZ, but also lacks fusion in the weld root and obtains smooth geometry at the weld toe. This ensures high static and fatigue performance for the whole joint. With the BD process, the end-product requirements can be considered in the manufacturing provided the optimal solution for the welding preparation. However, the lead time is now doubled compared to the single welding pass case but still shorter than the originally designed case with a throat thickness of 8 mm welded with three passes. In addition, the solution results in an optimal compromise concerning the requirements of the end user. Fatigue is the critical failure mode for the joint, and this solution obtains good fatigue performance to the joint even without postweld treatments, which means reduced lead time and costs. The BD process could be continued, e.g., by assessing the optimal welding sequence and starting points for the robotic welding to control both welding deformations and residual stresses, as well as weld quality, or it can even yield development of new advanced low-alloy UHSSs to sustain lower cooling rates without softening. The BD concept can include all manufacturing steps, but the most influencing phases should be identified first. Consequently, the actions taken are the most meaningful and have the greatest impact on the performance of an end product. In this context, welding can be regarded as a main manufacturing phase as it can severely change the properties of the semi-finished product. However, step by step, the BD concept can be extended to other manufacturing stages and consider more multiparametric optimization. In general, the BD concept can be regarded as a tool and idea, supporting the green and digital transition in the field of welded structures to provide sustainable and profitable business in green manufacturing.
Meanwhile, the BD concept provides many advantages and extensive computational resources are available, its implementation still initiates many challenges and requires a huge workload to be applicable. Even in the field of welding (BD) simulations, there are various parameters to control and vary, which makes the experimental verifications and, consequently, the optimization of processes challenging. The BD concept also provides multiple options for backward steps, and thus automized processing is required, e.g., using statistical approaches. Furthermore, as various tools and subroutines are used in the simulation of different manufacturing steps; an interface or database between various individual tools is needed to collect and consecutively utilize the same and produced information in different steps. Another challenge is related to the genericity of the BD concept. When utilizing the concept for finding the best solutions for manufacturing and welding production, the result is workshop-dependent, as the available resource and equipment should be taken into account. Furthermore, in the material design, the BD concept can yield, at least in its early steps, unrealistic and uneconomical material requirements.
In a conclusion, the BD is a novel and promising approach in the field of welded structures, and background work on supporting the applications of the BD concept has been already taken, e.g., by simulating different welding processes and posttreatments. However, the BD concept still requires a huge amount of work in order to comprehensively realize it in practice. Nevertheless, it makes sense to realize it step by step, starting from the most essential part of the production chain.
Funding Open Access funding provided by LUT University (previously Lappeenranta University of Technology (LUT)). This work has been carried out in the Fossil-Free Steel Applications (FOSSA) project (grant ID 5498/31/2021). The authors wish to thank Business Finland for the financial support.

Conflict of interest The authors declare no competing interests.
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