1 Introduction

1.1 Pipeline steels

Currently, there is a requirement to transport crude oil and gas by pipeline at a higher operating pressure to increase the capacity. This demands the use of high-strength steels. Increasing the strength of the pipeline steel enables a significant reduction in wall thickness with resulting reduction in weight. Thus, a major aim within the steel industry is to develop high-strength microalloyed pipeline steels (~700–800 MPa). It is, however, important that the increase in the yield strength is not accompanied by a decrease in fracture toughness and formability because a decrease in toughness will promote stress-induced cracking, and reduced formability will cause difficulties in forming (e.g., pipe-bowing). Thus, high strength in relationship with high toughness and formability are important requirements of the pipeline industry [1–3].

High strength–toughness combination is necessary for pipeline steels for transporting natural gas and crude oil over a long distance under high pressure [2]. Other characteristics that are needed include resistance to hydrogen-induced blister cracking in sour service environment [4, 5], stress corrosion cracking resistance, especially in H2S environment [6–8], and fatigue resistance [9, 10]. It is important that the microstructure of the pipeline steel provides combination of above-mentioned properties.

The evolution of microstructure depends on alloy chemistry and thermomechanical processing. Alloying additions such as Mn, Nb, V, Ti, Mo, Ni, Cr and Cu are commonly employed in pipeline steels to achieve the desired microstructure and mechanical properties [5, 6, 11–13]. However, sensible selection of alloying elements is necessary to obtain advantageous effect on mechanical properties with reduced alloy cost. For instance, the number of alloying elements is reduced to achieve lower carbon equivalent (CE) to guarantee good field weldability [2, 3]. On the other hand, alloy additions such as Cr, Cu and Ni are added to obtain strength in severe corrosive environment [2, 5]. Controlled thermomechanical processing is considered as the primary path for the development of API-grade pipeline steels because it provides the desirable and fine-grained microstructure. In addition, it allows high strength–toughness combination to be achieved with accelerated cooling [3]. The ultimate microstructure strongly depends on the processing parameters such as reheating temperature, percentage reduction, deformation temperature, cooling rate, and coiling temperature [14]. This is because fine austenite grains, substructure and dislocations in austenite effectively promote the transformation of fine ferrite. The primary grain refinement in controlled rolling is achieved through recrystallization of austenite during deformation and through the use of microalloying elements, such as Nb that precipitates as fine carbides and inhibits grain growth [15].

In steel-related research, which is also the focus of this study, ANN has been used widely to understand a wide range of problems including phase transformations [16], surface texture [17–19] and mechanical properties [20–23]. For instance, Trzaska and Dobrzanski [24] applied ANN to decide the composition of steel for achieving a particular hardness. Monajati et al. [25] used ANN to understand the effects of the processing parameters on the mechanical properties such as yield strength, work hardening and plastic strain ratio. Corrosion studies have also been made using the ANN [26, 27]. An overview of the application of neural networks to study material science problems has been demonstrated by Mukherjee and Singh [28] and Bhadeshia et al. [29].

In this research, ANN has been employed to determine the ultimate tensile strength. ANN has been used to determine the ultimate tensile strength as a function of eleven alloying elements(C, Si, Mn, Cu, Ni, Cr, Mo, Ti, V, Nb and B), yield strength (at 0.005 offset strain) and impact energy (at −10 °C). The theory behind the ANN configuration and the performance with regard to high-strength low-carbon steels is discussed in the ensuing sections. More precisely, using the experimental data of 104 microalloyed steels, the ANN has been developed to predict the ultimate tensile strength for a given set of input variables mentioned above.

1.2 Artificial neural networks

ANNs were developed to model the human brain [30]. Even an ANN fairly simple and small in size when compared to the human brain has some powerful characteristics in knowledge and information processing because of its similarity to the human brain. Therefore, an ANN can be a powerful tool for engineering applications [31]. McCulloch and Pitts [32] defined artificial neurons for the first time and developed a neuron model as in Fig. 1. McCulloch and Pitts’ network [32] formed the basis for almost all later neural network models. Afterward, Rosenblatt [33] devised a machine called the perceptron that operated much in the same way as the human mind. Rosenblatt’s perceptrons [33] consist of “sensory” units connected to a single layer of McCulloch and Pitts [32] neurons. Rumelhart et al. [34] derived a learning algorithm for perceptron networks with constituted hidden units. Their learning algorithm is called back-propagation and is now the most widely used learning algorithm. Figure 2 shows a typical architecture of a multilayer perceptron neural network with an input layer, two hidden layers and one output layer. As a result of these studies, together with the developments in computer technology, using ANN has become more efficient after 1980 [35].

Fig. 1
figure 1

Architecture of applied neural network [32]

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Fig. 2
figure 2

A typical architecture of multilayer perceptron neural network [38]

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As it can be seen from Fig. 1, an artificial neuron is composed of five main parts: inputs, weights, sum function, activation function and outputs. Inputs are information that enters the neuron from other neurons of from external world. Weights are values that express the outcome of an input set or another process element in the preceding layer on this process element. Sum function is a function that calculates the effect of inputs and weights completely on this process element. This function computes the net input that approaches a neuron [36]. The weighted sums of the input components (net) j are calculated using the below equation as follows:

$$ ({\text{net}})_{j} = \sum\limits_{i = 1}^{n} {W_{ij} x_{i} + b} $$
(1)

where (net) j is the weighted sum of the jth neuron for the input received from the preceding layer with n neurons, W ij is the weight between the jth neuron in the previous layer, x i is the output of the ith neuron in the previous layer [35], b is a fix value as internal addition and R represents sum function. Activation function is a function that processes the net input obtained from sum function and determines the neuron output. In general for multilayer feed-forward models as the activation function, sigmoid activation function is used. The output of the jth neuron (out) j is computed using Eq. (2) with a sigmoid activation function as follows [37]:

$$ O_{j} = f({\text{net}})_{j} = \frac{1}{{1 + {\text{e}}^{{ - \propto ({\text{net}})_{j} }} }} $$
(2)

where α is constant used to control the slope of the semi-linear region. The sigmoid nonlinearity activates in every layer except in the input layer [35]. The sigmoid activation function represented by Eq. (2) gives outputs in (0, 1). If desired, the outputs of this function can be adjusted to (−1, 1) interval. As the sigmoid processor represents a continuous function, it is particularly used in nonlinear descriptions, because its derivatives can be determined easily with regard to the parameters within (net) j variable [35].

LMBP is often the fastest available back-propagation algorithm and is highly recommended as a first-choice supervised algorithm, although it requires more memory than other algorithms.

2 Training and verifying

2.1 Data collection

Tensile test was performed at room temperature. Transverse sample were cut from body of the pipe according to API standard [39]. The gauge length was 50.8 mm, and a 0.5-class extensometer was used to measure the extension. The tensile samples were prepared according to ASTM E8 [40]. The impact test samples were cut, transverse to the rolling axis (according to API standard), from an area free of defects, machined and prepared according to ASTM E 23 standard [40]. The samples had the following dimensions: 10 mm × 10 mm × 55 mm. During the test, the samples were struck with a high-energy pendulum (750 J). The hardness test load was 10 kgf, and the test method was dead-weight. The transverse samples were prepared according to IPS standard [41]. The chemical analysis of elements in steels was carried out using ARL quantometer 2460 model. Sample preparation and test were done according to ASTM A751 [40]. Transverse sample extracted from body of the pipe.

In the present investigation, the artificial neural network has been trained, tested and validated for prediction of ultimate tensile strength of X70 pipeline steels. For this purpose, the experimental data of 104 pipeline steels with different chemical compositions have been used. The input variables of the ANN modeling are the weight percent of alloying elements, the yield strength and the Charpy impact energy at −10 °C. These parameters along with their ranges have been summarized in Table 1.

Table 1 The parameters and their range used in the artificial neural network
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2.2 Neural network model structure and parameters

ANN modeled in this research has seven neurons in the input layer and one neurons in the output layer. According to the API Specification 5L/ISO 3183 [39], the values for input layers were carbon equivalent, based upon the International Institute of Welding equation (CEIIW) (Eq. 3), the carbon equivalent, based upon the chemical portion of the Ito-Bessyo carbon equivalent equation (CEPcm) (Eq. 4), the sum of the niobium, vanadium and titanium concentrations (VTiNb), the sum of the niobium and vanadium concentrations (NbV), the sum of the chromium, molybdenum, nickel and copper concentrations (CrMoNiCu), Charpy impact energy at −10 °C (CVN) and yield strength at 0.005 offset (YS). The value for output layer was ultimate tensile stress (UTS).

$$ {\text{CE}}_{\text{IIW}} = {\text{C}} + \frac{\text{Mn}}{6} + \frac{{({\text{Cr}} + {\text{Mo}} + {\text{V}})}}{5} + \frac{{({\text{Ni}} + {\text{Cu}})}}{15} $$
(3)
$$ {\text{CE}}_{\text{Pcm}} = {\text{C}} + \frac{\text{Si}}{30} + \frac{{({\text{Mn}} + {\text{Cu}} + {\text{Cr}})}}{20} + \frac{\text{Ni}}{60} + \frac{\text{Mo}}{15} + \frac{\text{V}}{10} + 5{\text{B}} $$
(4)

Two hidden layers with 10 and 8 neurons were used in the architecture of multilayer neural network because of its minimum absolute percentage error values for training and testing sets. The neurons of neighboring layers are completely interconnected by weights. Finally, the output layer neurons produce the network prediction as a result. From the total 104 gathered date, 74 were randomly selected and trained by the network, 15 data were used for validation and the other 15 data were used for testing the network.

In this study, the back-propagation training algorithm has been utilized in two feed-forward hidden layers. Back-propagation algorithm, one of the most well-known training algorithms for the multilayer perceptron, is a gradient descent technique to minimize the error for a particular training pattern in which it adjusts the weights by a small amount at a time [38]. The nonlinear sigmoid activation function was used in the hidden layer and the neuron outputs at the output layer. The trained model was only tested with the input values, and the predicted results were close to experiment results. The values of parameters used in neural network model are given in Table 1.

3 Results and discussion

3.1 The effects of chemical composition

The parameter that has been most used in practice to measure steel weldability is the carbon equivalent (CE) formula, where good weldability is in general obtained by maintaining a low CE. This method of evaluation is based upon the empirically identified tendencies in the variation of the Martensite start (Ms) temperature as a function of the alloying elements present in the steel [39].

In the 1980s, the technical specifications for pipelines indirectly addressed the issue of weldability by the chemical composition limits imposed. According to the API 5L standard, the maximum carbon level for an X-65 steel was stipulated to be 0.26 pct, whereas for the X-70 grade, this maximum was lowered to 0.23 pct [42]. More modern high-strength low-alloy (HSLA) steels have been produced with a much lower C content of around 0.1 pct, and the tendency is to exploit even lower levels.

The current tendency to reduce the C level leads to a decrease in CE and reduces hardenability. For steels with C levels of around 0.1 pct, good weldability is achieved by the addition of appropriate alloying elements. The addition of Mn inhibits the formation of high-temperature transformation products such as pearlite and polygonal ferrite as well as promoting solid solution strengthening of the ferrite. Nickel, in addition to increasing hardenability, also increases toughness. Aluminum is exploited as a deoxidizing agent and, via nitride precipitation, as a grain refiner, whereas Nb serves to guarantee the precipitation processes, which retard austenite grain growth [43].

The addition of microalloying elements also contributes to the formation of martensite/retained austenite (MA) and thereby the weldability. Carbide-forming elements such as Mo, Nb and V retard the decomposition of MA. The addition of Mn, Cr and Nb lowers the Banite start (Bs) temperature and promotes the formation of MA. In the published literature, it is mentioned that the presence of MA can be considered deleterious to toughness. It has also been observed, however [44–46], that this deleterious effect is not only associated with MA volume fraction, but also with its morphology, size and distribution in the matrix.

3.2 Artificial neural network modeling

In terms of simulating the heat treating process using ANN, one should consider that the physical simulation by experimental work not only is time consuming but also cannot overcome many errors encountered at a laboratory scale. Hence, a well-established ANN modeling can allow predicting ultimate tensile strength with the capability for replacing even mathematical modeling. The current ANN model adopts a nonlinear mapping method to set up models according to input and output data directly. In this respect, extensive research activities were made to optimize many industrial processes using ANN. The obtained results can be discussed as follows: First, the use of artificial neural network exhibits excellent accuracy in predicting the ultimate tensile strength outputs. Secondly, as already stated, there are many contributing factors in ultimate tensile strength that cannot be considered in the mathematical modeling, but they can be easily incorporated in neural network modeling. Thirdly, the present artificial neural network can predict the mechanical properties directly and in a much more rapid approach compared to the mathematical modeling such as finite element.

These characteristics of present ANN in predicting the ultimate tensile strength can be very precious from an industrial point of view. A network with four layers, seven neurons for the input layer, 10 neurons for the first hidden layer, 8 neurons for the second hidden layer and one neuron for the output layer was designed. This combination resulted in a feed-forward neural network that requires a back-propagation algorithm. As already indicated, the input variables for establishing a new ANN model were considered as chemical compositions and yield strength and Charpy impact energy results.

The trained network was then used to compare the predicted and measured values. These comparisons are shown in Fig. 3. In these figures, the ultimate tensile strength values results. As it is obvious, the values predicted by ANN are in very good agreement with the ones obtained by experimental work.

Fig. 3
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Correlation of the measured and predicted ultimate tensile strength values in a training, b validation and c testing sets for ANN mode

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Figure 3 presents the comparison between measured and predicted results for ultimate tensile strength levels. The agreements between the predicted and measured values indicate that this approach can be very useful in modeling the mechanical properties of steels. That is because, in all cases, the prediction values match the measured amounts very well. Once more, this clearly indicates the accurate function of the trained ANN in predicting the ultimate tensile strength. Consequently, the developed ANN model can be used to simulate and predict the ultimate tensile strength of steels. As mentioned earlier, the complexity of thermomechanical treatment, due to interacting many parameters simultaneously (e.g., material composition, applied strain, strain rate, austenitizing time and temperature, cooling rate), can make it difficult to get accurate experimental results in this regard.

It terms of the contribution of errors, it is worth mentioning that the errors are inevitable in any approach. However, there are always shortcomings that can affect the accuracy of both the measured and predicted values. These can be, for example, nonuniform microstructure in the specimen, inhomogeneity of the mechanical properties in the samples.

In this study, the error during the training, validation and testing in ANN model can be expressed as absolute fraction of variance (R 2) which is calculated by the below equation [47]:

$$ R^{2} = 1 - \left( {\frac{{\sum\nolimits_{i} {(t_{i} - o_{i} )^{2} } }}{{\sum\nolimits_{i} {(o_{i} )^{2} } }}} \right) $$
(5)

where t is the target value and o is the output value.

All of the results obtained from experimental studies and predicted by using the training, validation and testing results of ANN model are given in Fig. 3a–c, respectively. The linear least-square fit line, its equation and the R 2 values are shown in these figures for the training, validation and testing data. Also, inputs values and experimental results with validation and testing results obtained from ANN model are given in Tables 2 and 3, respectively. As it is visible in Fig. 3, the values obtained from the training, validation and testing in ANN model are very close to the experimental results.

Table 2 Data sets for comparison of experimental results with validation results predicted from the ANN models
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Table 3 Data sets for comparison of experimental results with testing results predicted from the ANN models
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The result of testing phase in Fig. 3 shows that the ANN model are capable of generalizing between input and output variables with reasonably good predictions. The performance of the ANN model is shown in Fig. 3. The best value of R 2 is 91.58 % for training set, and the minimum values of R 2 are 91.3 % for testing set in the ANN model. All of R 2 values show that the proposed ANN model are suitable and can predict UTS values for every age very close to the experimental values.

4 Conclusions

An artificial neural network model was developed to model and predict the ultimate tensile strength of X70 pipeline steels. The values predicted by present model are in very good agreement with those measured by experimental results. Therefore, the present ANN model can be used to predict accurately the ultimate tensile strength of X70 pipeline steels. ANN models will be valid within the ranges of variables.