How many Infrared sensor modules can be added to a single Arduino (eg;Uno)
You just want to know how many you can attach to an Arduino board or how many Arduino Uno boards you need, but it does not work like that.

Some sensors with a led require 5mA or 10mA or 20mA. The reflective optical sensors use a IR (InfraRed) led. The Arduino Uno 5V pin can probably not supply enough current for 40 leds. Therefor you might need a seperate power supply.
I think the TCRT5000 is typically set at 10mA.

The Arduino Mega 2560 and the Arduino Due have many pins. But with 40 TCRT5000 sensors, the total current is too close to the limit.

In such situation often extra hardware is added. You can use one Arduino Uno board, with extra hardware for multiple inputs or outputs.  

An "expander" is a chip or a module that connects to the Arduino with a few wires, but has many input and/or output pins. For example a "expander" with I2C interface to the Arduino Uno as mentioned by @matsk. Although a I2C expander has a slow I2C interface, they are sometimes smart and can tell which pin has changed by reading a single byte.

"Shift registers" are chips with for example 8 input pins or 8 output pins. The data of the pins is shifted into the chip with a data and clock signal. There are many examples for that: ShiftOut with a 74HC595.

A analog "multiplexer" or "mux" is a chip that can connect one common pin to one of 8 pins. The signal can go both ways. Nick Gammon about a multiplexer.

A "ADC" is short for "Analog to Digital Converter". The Arduino Uno has an internal ADC, but also a external ADC can be used. They have often more than one analog input.

"Polling" is when an Arduino is reading many inputs continuously one by one. If for example it takes 5ms to read a sensor, then 40 sensors take 200ms. That means that every sensor is read once per 200ms. If a train would pass within that 200ms, then it might be not detected.
The opposite of polling is with interrupts. If an external event happens, it could trigger an interrupt and the Arduino can react right then at that very moment. However, 40 interrupts is not possible.

Conclusion:
The best way depends on your hardware and software skills, on the maximum interval that you want to read the sensors, on the sensors themself, and how far apart the sensors are, and if you want 40 wires to a Arduino board.
The best Arduino board also depends on what you want to do with the data and what else the Arduino has to do.
Some sensors have a analog output and some a digital output. It depends on your situation and the way the train is detected.
If possible, then I would choose a solution where all the hardware can be easily be replaced. If the sensor has digital outputs, then I would connect them to a Arduino Mega 2560 or Arduino Due.